2/4 Introduction to categorical logic, classifying toposes and the "bridge" technique (IV)
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2/4 Introduction to categorical logic, classifying toposes and the "bridge" technique (IV)
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Title 
2/4 Introduction to categorical logic, classifying toposes and the "bridge" technique (IV)

Title of Series  
Part Number 
4

Number of Parts 
28

Author 

License 
CC Attribution 3.0 Unported:
You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
Identifiers 

Publisher 

Release Date 
2015

Language 
English

Content Metadata
Subject Area  
Abstract 
Introduction to categorical logic, classifying toposes and the « bridge » technique Construction of classifying toposes for geometric theories. Duality between the subtoposes of the classifying topos of a geometric theory and the quotients of the theory. Transfer of topos‐theoretic notions across the duality and their logical interpretations.

00:00
Lecture/Conference
Topostheorie
Range (statistics)
Algebraic structure
Right angle
01:08
Category of being
Group action
Theory of relativity
Thermodynamisches System
Meeting/Interview
Lecture/Conference
Multiplication sign
Weight
1 (number)
Algebraic structure
03:20
Point (geometry)
Multiplication sign
1 (number)
Mereology
Event horizon
Mach's principle
Prime ideal
Regular graph
Lecture/Conference
Game theory
Newton's law of universal gravitation
Process (computing)
Weight
Model theory
Inverse element
Basis <Mathematik>
Special unitary group
Line (geometry)
Binary file
Measurement
Higherorder logic
Universe (mathematics)
Right angle
Game theory
Maß <Mathematik>
11:28
Computer programming
Group action
State of matter
Multiplication sign
Equaliser (mathematics)
1 (number)
Sheaf (mathematics)
Discrete element method
Rule of inference
Event horizon
Grothendieck topology
Frequency
Sign (mathematics)
Uniformer Raum
Manysorted logic
Lecture/Conference
Natural number
Operator (mathematics)
Set theory
Directed graph
Area
Pairwise comparison
Geometry
Physical law
Algebraic structure
Nominal number
Special unitary group
Incidence algebra
Mortality rate
Binary file
Equivalence relation
Arithmetic mean
Universe (mathematics)
Order (biology)
Phase transition
Right angle
Game theory
Maß <Mathematik>
27:26
Geometry
Theory of relativity
Moment (mathematics)
Materialization (paranormal)
Mereology
Category of being
Arithmetic mean
Algebra
Lecture/Conference
Wellformed formula
Logic
Natural number
Genetic programming
Right angle
Musical ensemble
Descriptive statistics
Directed graph
29:35
Area
Functional (mathematics)
Nuclear space
Structural load
Maxima and minima
Mereology
Time domain
Equivalence relation
Quadratic form
Category of being
Mathematics
Thermodynamisches System
Lecture/Conference
Logic
Wellformed formula
Object (grammar)
Gamma function
Social class
Condition number
Newton's law of universal gravitation
35:24
Geometry
Functional (mathematics)
Logarithm
Equaliser (mathematics)
Multiplication sign
Perspective (visual)
Hand fan
Theory
Product (business)
Wave packet
Element (mathematics)
Frequency
Mathematics
Uniformer Raum
Lecture/Conference
Wellformed formula
Operator (mathematics)
Ideal (ethics)
Analytic continuation
Condition number
Morley's categoricity theorem
Independence (probability theory)
Basis <Mathematik>
Lattice (order)
Sequence
Time domain
Numerical analysis
Substitute good
Category of being
Arithmetic mean
Logic
Order (biology)
Object (grammar)
Identical particles
Family
Maß <Mathematik>
41:07
Geometry
Functional (mathematics)
Group action
Direction (geometry)
Equaliser (mathematics)
Correspondence (mathematics)
Maxima and minima
Division (mathematics)
Kontraktion <Mathematik>
Rule of inference
Mach's principle
Order (biology)
Uniformer Raum
Manysorted logic
Lecture/Conference
Wellformed formula
Descriptive statistics
Social class
Area
Theory of relativity
Generating set of a group
Model theory
Algebraic structure
Grand Unified Theory
Lattice (order)
Axiom
Variable (mathematics)
Quadratic form
Equivalence relation
Universe (mathematics)
Right angle
Maß <Mathematik>
45:45
Point (geometry)
Functional (mathematics)
Multiplication sign
Maxima and minima
Power (physics)
Element (mathematics)
Explosion
Gaussian elimination
Sign (mathematics)
Uniformer Raum
Lecture/Conference
Wellformed formula
Geometry
Theory of relativity
Real number
Model theory
Algebraic structure
Lattice (order)
Variable (mathematics)
Equivalence relation
Connected space
Vector potential
Category of being
Angle
Symmetry (physics)
Logic
Order (biology)
Object (grammar)
Resultant
Directed graph
Maß <Mathematik>
51:23
Group action
Hecke operator
Eigenvalues and eigenvectors
Logarithm
Multiplication sign
Maxima and minima
Insertion loss
Propositional formula
Explosion
Frequency
Mathematics
Strategy game
Meeting/Interview
Term (mathematics)
Wellformed formula
Genetic programming
Associative property
Set theory
Descriptive statistics
Condition number
Addition
Geometry
Theory of relativity
Real number
Model theory
Sequence
Equivalence relation
Higherorder logic
Category of being
Length of stay
Funktor
Logic
Summierbarkeit
Object (grammar)
Musical ensemble
Local ring
Maß <Mathematik>
56:53
Model theory
Insertion loss
Incidence algebra
Sequence
Grothendieck topology
Element (mathematics)
Category of being
Sign (mathematics)
Boom barrier
Thermodynamisches System
Causality
Lecture/Conference
Meeting/Interview
Natural number
Universe (mathematics)
Gamma function
Descriptive statistics
1:00:30
Axiom of choice
Functional (mathematics)
Observational study
Logarithm
Multiplication sign
Quantification
Maxima and minima
Solid geometry
Student's ttest
Mereology
Event horizon
Grothendieck topology
Frequency
Lecture/Conference
Meeting/Interview
Flag
Series (mathematics)
Condition number
Injektivität
Area
Standard deviation
Geometry
Model theory
Algebraic structure
Complete metric space
Sequence
Quadratic form
Category of being
Boom barrier
Universe (mathematics)
Object (grammar)
Local ring
Resultant
1:06:47
Group action
Multiplication sign
Euler angles
Sequence
Category of being
Boom barrier
Lecture/Conference
Network topology
Strömungsdrossel
Right angle
Identical particles
Associative property
Multiplication
Set theory
Condition number
Physical system
1:11:46
Presentation of a group
Correspondence (mathematics)
Model theory
Independence (probability theory)
Measurement
Rule of inference
Equivalence relation
Group representation
Invariant (mathematics)
Lecture/Conference
Logic
Universe (mathematics)
Summierbarkeit
1:13:59
Point (geometry)
Classical physics
Multiplication sign
Model theory
Rule of inference
Sequence
Grothendieck topology
Goodness of fit
Computer animation
Thermodynamisches System
Lecture/Conference
Different (Kate Ryan album)
Universe (mathematics)
Right angle
Condition number
1:16:16
Computer animation
Manysorted logic
Lecture/Conference
State of matter
Real number
Modulform
Parameter (computer programming)
Total S.A.
Resultant
Junction (traffic)
1:17:27
Geometry
Pairwise comparison
Existence
Kontraktion <Mathematik>
Grothendieck topology
Group representation
Lecture/Conference
Logic
Calculation
Object (grammar)
Bounded variation
Resultant
Maß <Mathematik>
Physical system
Condition number
00:00
what I and there is room for her work in her the head is seen you go in and out of moderates in the we will have to be isolated cases last year was that he had been what went on at the top of the range of Of course we see the and and have a seat at the in the city of Los Sudan immediately that even after it was found that less than that years and the right to see the structure of the EU Louisiana structurally indicated on the eastern end
01:09
of an even more than in the same time the idea was that the
01:16
head of the structure the 1st was the worst in in the nation it was the end of the evils of dancers on the activities didn't want to and that is what what you not want to be anything more than had the Bloomberg complimented him on the head with movements on Mall is all that is if you give the knowledge of of the same year the NEA and also suggests that the agency had access to the rest of the season In general the the relations
01:59
following is a yes yes and those were the days later in the day he said in in an environment in which the group not only will you have to do that in the end I saw you in and on and on and on on the eve of the and then on the morning of the hearing is the net and lighting then this is what it is that you the letter of the 1st as the new leader of the unity that he is the head of the American was show at the medical center including the 1 that was used to cool the property and the occasional on it and then you know you have to use this season so
03:22
you would look at these things I was in the hands of the the following
03:35
year on the eve of the idea year we have it president of the Soviet Union and the people in of the United States in and out of and you need to have a clear and ordinary people the end of the year and duties of the easing of the regional presidents and prime ministers and the head of the government and the people anything but that it would not be he has been on the basis of the made the move because it is part of a lot of land and he's easy to understand is that the In the case of these things the fact that they have and now and you will have a solution that the researchers have reason to think about that will show the world he said he said he was not on the side namely will know that he said even you had also called on the Government of of City could also found that there was a wonderful thing this point because unity that is that is just not going to let him go ahead and this is not the only 1 in the world and the news that the timing of the it was in the season and is is the best for the man he said and that means something to you that you also have the support of our time in history as another as is the is the university last year as the people in the United States of using our resources they need to cancel as you would need some new measures the air is not and so on and on doing anything you want to pass on to the end of his life in his own words the that the United States over these properties of movies that we we had to go with his original sentence and motorists and Angela I need you I mean it was part of the world because this is what he said was full of things that people in the world that is those that he's not here at the back end of the the juvenile and along the Easterly sees itself and it has you have to choose that is the hole wall and deceased without you will always know that someone had and these are good the policy what do this is the right yet I have he been working at the University of movies as well as I about this I don't use I don't know what they're going to find limits and that the directives of if possible have signed on in support of cesium and of organizers the units on the ground in the office of problematic excellence is something that I want to comment about firms from what the Net in the case it of the year in 1 of what was the son the of and being here I have to do this is the only 1 name of the game and I was on the way you know don't what they have sold and sometimes it so you have to the problem that the right write to and and then you have go they also know that there is no and I think now is the 1 that that you get involved in all of the leaders in the structured in the sense that of little that kind these are some of the Ugandan that and saying that the people of Iran is also process and he's the best the event radicalizing mediation the head of animal model year highs he is already so dizzyingly had gained support from the government in the early on that then line and you want the sun In the last year of his involvement in in the this is reason and then they face and then go into a fund businesses and using data was that the user of the Internet and the England
11:28
was easy on the walls of the Old the and NYT is not because it is in the idea construction of 1 of the new law the qualities that I recently had the easiest time and an he says he has found and you basically the same as that of the people we have to good I needed them much of the area of outstanding orders of 100 years he said that so far this right the history each fragment as so and so we will have to use there this is the way to the area which holds the EU's a sign that the economy In food Luis resizing and it has in the sense that the monitors of the relevant to the kind of Europe and the know Department of Surgery all unit found that there was robbery was from around the world trade and the sentiment that major major seats on salt in Galicia course the very few although is not candidacy status saying that the fact that more than a month and that you have personally because of the presence of of the season the scene at the end of the year and provide support for the book this is in the southern Sudanese and it's there I wasn't it yeah I mean I was so we thank them for the use of all all I want to do is get really most the knowledge on the other side of the the money will also said that then you don't see it as a sign reading but there is hope that everything is out of it was the site of the people in the world said it was "quotation mark and it is not the case from the beginning that solution it was not until the end of the day we used to say that in the next year the unity of the people state of the development of the world have not this time some of the people who grew up in in that year too you need to the new groups in our head I have the honor of itself bodies of the anyway In the end the on you not since Nixon who was in the game of the world and the current law and the beginning of the the what would you think that I have no reason not to a it history world with the union will they have a lot of reasons reach the title of think the some world's most the and it has been involved in any of them I can't believe this communication information he became the 1st American Financial Services program room during his years at the top of the world and I have always sold here and we have these funds and singing along its someone is a little about the nomination how to find out what's involved in this section of the country and Asia the government I just wanted to give you examples on the Net Institute of America with the use of images status as a listing on internet media after the location of the the nature of the sun and the stars and the other new rules the unity and solidarity of the operation of the moves that will not be moved at to the University of over anything in the way of the world and the world there was and that he had received a call about disposing of any and using it the government is now sold in the UK and the soldiers I have a sense that this was not the end of the the faces Oregon and the handling of the a ride on the end of this century or only in the event of a major body and then they find 1 that wanted peace and the unity more than United and international structure will monitor the situation in region and is the acting governor of New England was this status from the city of the year the most of the but there was no evidence of that in any and all of the you see I
19:30
have to have a lot of past the notion that evening he wants to go the and that was it laughter from the United States announced this what penalties usually easygoing nature of some of the people you soundness of the group 1 of the centers in all this is that it has only that's about it Of course it is also interesting things about this is that locked out of the final say in the decisionmaking that again we have in the face of of the set and trying expect and endangering the nations of the world and that the state had something in his that the only about 4 times in the past was in the U.S. Senate and the provision of security and the war in Iraq since the 1980's anything and I mean all threats I'm not going let you know he is the kind of thing and that is not insisting on the horrors of the past year and a half of the year world's of the In many ways originally wanted him out of the city and a little something useful in these days I mean you have to and even the mediation of this sort of incident the OK and so I think I was going to be when he stays all the amazing thing is that we have a lot of money he said he was so unique and hearing and leaders of the day it was announced that have ended the week in the Soviet the I'm looking at the him borders you I had been used along but the view of most yes No he's he's in the a middle and the year mission who are even walking in on the use issue was also used as identification of safety at all and even fewer have testified he was not main problems here specified not so intense that it is more nature only those he wanted something more last year we had it's it will be a reality examples of this initiative and the last time you can't just you she a sense but rather refusal of ratings or other kinds of all Novotna beginning to encourage the Fed technology during the customers and the government because that I consider issues of science and engineering marvels and that you will ,comma sheets of roofing that don't want that the EU enlargement of the EU side the book and he was locked in a storage unit like means but also of wanted to say this year have she's all the stadium located amazing assessment of his books are areas that it said it had been a member of the modernization of the new year east side and of the north of the Indian media executives and will you really have rejected this she's our motives of using and various periods in which the results or in this section is full of it because I had a lot of people intent to you and I saw that in the year of the Chief of all of them all these years is chief the soldiers on and equality distorts history on all the laws and you will hear all of this that was just going with the political effects of the global soldiered each appointment was the the successfully against you the interesting and it's all these finds that these are the was it's a lot more and more than a year this "quotation mark all right so you see that in fact he was by the time I will say just a few cents and will be orders this year as seen on the ground that might wall of women and the whole bunch of mullahs originated here in the next phase of incense and then you will see that justice is that it is the primary thing was 1 that was in U.S. in on all the insiders sold under the suggests that similar considerations in just 1 year in year at the usefulness of the name of the University of the said about them and you can have what was the the wasn't the need for that compared With all the little not just once in the back then was that all of this means that even imagine all these reasons Will move on this In this belongs comparison is the at this hearing will be resumed on the house of using your government the yes conclusion you and not the of year the school things which are required to have that that's not only because the militants the fact that he is not his and my friend who is in this is that England and also said he and his father that I wanted to hear it reviewing the data on the use of for the day when the Americans and the set it is a ruling was the reply so I don't think there will well if would allow the let's let's look back not only is that's where it's safe the efforts while his party and his unit to
27:26
advance toward the meaning of Ontario completely syntactic on Monday is
27:33
knowledge of course is this I had the experience of the past 2 year has since we can of course that for users of feeling old categories defeated his materials among categories if you want to formalize it you will have the country's infuriated because there if you want to formalize the composition of TWA rows of seats in the composition is not always defined because it's only been trying to win they could only the 1st the coincides with the winner of the 2nd on the way to formalize his music that many baby and solidarity predicted for composition which is something like the Medicaid is a synonym for relational single so the season that ended relations symbol and there which expresses compositions of the meaning of badlyneeded the ages of given this composition and of course we will have that in the 1st column the equal and all manner of gene then it disease there and then existed and that is the nature of such a thing In the summer through 1 moment and what Quinault because you can't tonight it because you cannot deny that he had a unique moment in that says that it is unique so you have the right to see the same thing and J. H. Prynne I encountered at the end of the year so as to see the season contagion fury OK now I have given the examples as on how we can give description of saying that the company is yet to yes the knowledge is not part of the formula that is incoherent logic it isn't going intelligent because England logic you have the fullest and you can
29:36
buy 0 equal 1 implies a forwards so it isn't going and logic it is
29:42
acquiring here you can formalize it is acquitted because you can say that the text plus 1 in the implies a extramarital or from in the thing we so and the Senate seat in nuclear and religion so this is an emotional coloring look environment as it is it is a clear view of working with I think you From the in which and he the diesel fuel my sense provided that there is a kind of whether or not it is likely that needs not the finding exactly the same way as know about I mean it's a stand of its leader we that he had I about to what the 1010 was that there was not there and the fall of the formula has not been enough to specify the fragment that is what he was saying so I think this is a market that's going and what they need the impact is the it's OK and has softened organized so you probably make leave and now "quotation mark OK so national syntactic doing so intense that had 1 notion saying that the company for basically each of the comments made by the league and there no adjustment of Harper's administration I'm willing to give it a condition for the genetic fragment and then I will say modified to prevent the wonderful regular continued and incoherent OK so what these as saying that the company might want a genetic here because these areas that we have said that they are in the said and a new president saying broadband because there are so basically shows that there is 1 place where the syntax and semantics of the few meets the winner and which generates on the animals it's because as we should see from the way this equivalence is defined ending more than we need imagine all of this universe unloaded on the front of preserving the appropriates OK so it's even initiation saying that the company origin at hearing so supposed that the key is the Germans income all the signature signal so define this as saying that the category we have to specify what for the objects and the hours that the objects are popular as generated formulas that although the signature of the feeling he's sitting in a given context the sole negotiator while for the context and the formula together performance in objective so that the Committee for change the context that we had a different objects it's an important we might this and they want to consider so aptly naming equivalents and unify just changing the name of the writing was on the wall of the object which marked the end again and these are the objects and there was a of them while the IRA as part of this is likely more sophisticated New Hampshire Connecticut an older and formulas that Giuliani has always stood in Genentech a formula on you know and in the context of usable as a powerful simplicity of life installing a new principles and the texts and and why disjointed and who you think all formula hasn't here and which I approve of the functions from the dominant political domain so what does it mean the provably functional and you don't you actually they get equivalence classes of such formulas for technical reasons on Monday dedication she did that identifies formulas over the same context even the of equivalent of interfering in case we will take equivalence classes of such formula as this 1 of the areas I was saying that they are required to meet people that many functions ,comma Mason told it's what is eating up when I have told you not to understand what's going on here that you have to think equities semantically meant
35:25
what you want is that when you think is certainly that more than an email that you will be able to interpret the this Basic as asserted that civil justice so stated only only some of it believed that and in the same way you will have a jury on the other side and what you want is the NRO here so you want basically as to the some conditions at the prophetically medicine tactically that we change so that will take in the interpretation of this formula which will be there see sponges easing in the where was so it's interpretation we need is number is an object of the product of this Center for and the and solidly mediation Internet but he wanted the situation to come from an and there and that he had had the conditions that to 1 of its own in order for the slow so fast that condition is the fact that if you have something in Henan and there should be something that there is associated to eat that fooled the cell function it's a it's a light means that the Europewide perspective you go to the functionality dioxins in just a minute then in sequence falls so this is the 1st and then of course you want to edit the EFA something is investigation and then on the issue of the projected on 1 hand it to the domain only other end the government and so on the shoulder the social mutual on and then at the summaries Meza the Wonderbra characterized the functionality of the fact that the iconic signed between elements of the domain of befriended him and sometimes will likely is it that if I consider this and at the same time year don't the change the that I just make a substitution I want the American Lisa was finally quieted all of sequences should become 1 of in the united that see by soundness of the family was a Salomon Smith we but what about near the fact that you can easily book that exists the good of sequence and show them that when you think of interpretation we have them in our view union so it is completely stifled wanted to define identities and composition in discussing so I would have to do it that I think it's pretty clear that Atlantic accounting and that and as a player and it's also not Mohammed Hussein that this category is a dramatic because musically is the all named in here you really had the unification misdemeanor and logic and geometry that growth in the was admitted between logic in category fearing that the equalizer and were being used in these facts require this tonight because it is seen in the logical logical operations of transformed into categorical operations sequences there and then disjunction also need to be meaningfully becoming units of soldiers their data in the intersection and then made the conjunctions McCann intersections of so obviously you see that that there is this unification between us and the logic and the category theory that these are magnificently realized there might be some emotional saying that the category in which is knew to the Montreal the quarter although category logic which was actively involved in the 70's and solace and the categories of course are important also for leaving the classic .period was promoted as we will within minutes was the motivation for moving constructing justifying used to define saying that because proposal made maybe you wondered that I mean that the people that needed this somewhere mostly McEnery yesterday to publish this training them all Posada logic maintained 77 and involve costly on the evening of being only 1 to work on the basis of the making the selling is OK you have to know where your and my category and see where we during the meeting the humanitarian ideals and then there was the known annoying cell and there on the floor of the year the Yankees independent U.S. cities said category although he that's meaning soul it's like saying I think the continuity of the we know exactly OK so it you know that you have to prove that the
41:07
highest of pharmaceuticals unit that allegedly interfering with the rule in the I always 126 people in the
41:19
world that people who the world yes of course you can also ideas you can only stay community here he she warned you would probably think about it tomorrow they have the feeling that I was equally well on its way to be not abuses in the sense of constantly said Yeltsin's that of course you always came alone .period anything no I don't understand that is always better than you have a meaningful should now operates through here because this is the year yeah worry is on Monday introducing there's an equalizer and equally finding on need to invoke the notional prevented interfering wide so I sent back again continually you can be seen as a structure presented by generators relations if you fall on the Societe Generale said that industry now has lifting cemented the languages of amended the signature of the fuel is able to express their and their delegations that can be seen in the axioms of material marginally more parents than what was you interfere there from there and from there to the finish you can see he's OK so long now it well it looks at it In the or so now I change it and make a substantive trying to reduce the fat there so yeah I actually have already strained variables and will have a weakness of yen on their the engines that we shouldn't speak amendments just 1 of the men and newly amended corresponds with the exception whom he said OK and so on now always come back to this agreement is some knowing how are convinced them said we are watching the geometric Pondexter British sold here nearly have geography so geometric contracts here and so on are you win 1 that I know that we have defined the sort you might wonder how this is defined knowledge is defined in a most unusual way whether it's astounding oneday option because we can do it immediately from the other direction with the the description of the universe and model of the fury inside the city now in action that European going this way to looting in more than and all will be defined in the front there is Mary but the window associated with this morning when the most obviously include more usable associated just that the interpretation of the formula in any given 1 right so it makes sense to think that all the information about the modeling is actually complained that in the front associated with we should see that this is a case that has been through the end of the meeting and identification of noting Sunderland on the fury lying in the the army In an assessment that we can only hope that the finding that when we call it the empty universe although came 2 and when the anatomy of housing in the pool the equivalence classes all the formulas that approval functions area a 9 1 group said I am working on
45:47
landlady warned I and by what they have had to see you will get the final narrowing so it is down to
45:56
see I narrowing designed a continuing and maintaining the center and I mean we will be find the items in the saying that category in order for the Senate to mean to give us a company with a fine and meeting thing get now flies he said and when you get in centurieslong connected soul it's fine yes you don't it's not smaller actually but it is essential as more so it's enough it is equivalent equivalent of the sole international when power category sold some of out this season and are essentially will also a union Indiana laughter is this is just as it may seem that it is equivalent to 1 is more categories morning that it is business sold him and of course it is you only need the 191 human refused because of the fear that endangering the other cases it is always the rightful wonderful and prominent poses OK angles OK it's always had this kind of an open more Indiana they actually see who I would like a starting from a from talking to reporters in modern history with movies that is a point behind the founder president and monitored we shall apply different precisely this morning so we are now going to fine the so in order to define a signal structure and what we have to to believe that we have full specifying where the source added function singles and the elimination of the no sold stock a I'm I'm going to interpret this as I'd taken variable also a and acknowledges the formula to function seamlessly was intended to have and functional Xinhua which takes up his influence source of these kind and so yeah I think it and this is isomorphic and I had to the final and then and willing to work I simply think that in the summer so you see the season certain functions because any more functional than bigger functions and roles so it is certainly function associated it is in our unit is saying that the country and refusing to potential of my functions in the agency most of it says that you know who also has completed complete their soul so you see in the center of a result there about that this said represent the beauty is in the same time the media and extremely important and sometimes adulterated things can be uh uh yes is an example so I will say that continues in the requiring that it time new wearing their improved because they have any president ability of the fund there is always a very good news because it means that all the information about Hungary's containing just 1 is convinced that evening in 1 object 1 element and so is the defines the injury can complain and not an information yet we have the semantic search to find some of the furiously estate contains all the information the fact that you know that everything is actually convinced that Endesa universal model and a sign that the company is really striking any associated the war fearing because it shows that the basically the center of symmetry from which you should look at the hearing is not that the 2nd models there's 1 is used between classical logic but it is really a diesel tanker the commodity OK so just complete their relations single as well including subject of this thing so you consider just same condensed you just
51:24
hope that are unionized easily in and this is a symbol jet and so this was the year of the than professional relations works and how it is equally their total logical to verify that the genetic sequence and that is a valued in this more than it can only happen this pool in the fury I don't think you because it's very important body and being there and seeing if and only if it is probable that singlemindedness and just saying that it's a dramatic a sequence over the language of the fearing an overbooked being and yet you can immediately see the burden because of the way and the musical strategies regionalization and for those of you all of them in the mountainous challenging reporters proposition OK so now that we have the condition on the City University London we can complete the description of this equivalence of categories and because because we can also specify only works in the action and in the end and then action within hours of his simply too dangerous after ankle sending them to have come up behind them units the millenium leaders know that America seems to have his room at the end of the season molded by applying effort to resolve that we a model of so we are not here and there we have already had the lead the syntactic accounting worries In America isn't needed because I've got a functorial understanding of modern set and all eating a certain the set and the leader of the opposition it was this will on the addition to was that we on the debt the community very embarrassing to user that panel that the memorial for just the plastic and saying that the company was so just don't wander about the violence along with the under fragments logic this is interesting because they will give us some that ways of meeting the classifying the locals of our feeling now all while I'm just in terms of innovation Association during the period the wellestablished countries periods and you know what that is and the conditions and that the category of like this with copy of it and hear it may settle it's exactly the same construction accepted that that instead of taking genetic formula a competitive exactly the same nothing changes seemed fitting for a period around or redness and just below speechifying for clear and they will wrangling that and fraudulent because we simply since this is the time and that use of most interest to us I will not be any objective here I just write this heating OK and while testifying was a sum that so far we have conceded that numerical yearround may be found because about the people want what we needed was an example of this that as he has already been spent the day at the notion of some of Murphy's into consideration notional regimented working and they will be enacted at the university in Japan because of new medical fees and some human again so we will walk in the fragment all the geometric logic but they still so what are we going to easily we can consider the service to fund government assigns the future not only stop the category of modern certain on the fury inside the 3rd and that if we change it at all costs rise and more feasible we will have found knowing that in the other should you might action on this that and the fundamental issues the goal of the inventory school and will category lodging industry and intensity is there for a during the period of individual liberty .period hazard take justifying the global also which is defined as an adult also meant that agrees and said the steps in the front of Sudanese and that there on a major medical refuses from independent focused so I will call at the 18th to classifying the loss of the unit a categorical equivalent somewhere the
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models of the fury in any
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nature natural so this is not the furious and what is interesting about this feeling is that the the construction as a reconstruction of the universe and models and a sign that the government is completely for for wanting this incident is completely can only guess and you and what you all of you know what I mean you need to a site that because the government still was he so you have to define and then the lower side solar systems of adjustment which and we we sites so "quotation mark basically decent classifying the loss of the season did not invite the keeping of Jesus and that the category that we have just knew that we had not expected the predictable the Bollinger which is basically become accountable origin on discovery and which admits it completely explicit description so you are basically I think it would be a description of the 7th according so suppose that you have a seat on the New York saying that because company we had to decide when it is cold about so you supposedly things like this yeah so you stated that the summer it is coloring on the it can only help this sequence In will this sequence in which says that recently intriguingly says that any elements here should that the session beating market than in the environment here should come from some elements of the size of the year and the year of the this says sequence of about In so you see it that anything less than the future of this kind of he said it was an United will be 1 using things that as what about the fact that it is going to go with the census Paul Wilson the cause of peace on side of the understanding that as that date convenience for from those owner of the leader this is the season of the year and we believe that the there was no political agreements because the people who did most
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of the this is 1st that these are the the people that I think are elected version of it for like so
1:00:32
those mean on you if you look at the elite that actually use the stuff of science to prove to me that that is going on is already dead and now we have to find set well a context that now I'm not going to deal with the fled the front are because we don't even need because nowadays would having received his confusion and in the case of a condition category flat that is the same thing as confusion solid and we are going to apply the decent food and it's only get the phone vigilant they can refuse from Italy easy to the cells the same thing as in their completion Jake continues thousand from seeking a friend of being a 1980 continues it means that it sensors and JET covering 620 market and that you realize how easily then this is the same thing as envisioned in exactly the same thing and salt from the slot you granted to them all this as missile and this is our sidewalks and interestingly the user comments that they to this hearing is the fact that the aim of the because he's not going find that was of something and the wastewater facilities that you have to choose a side and so playing in the Washington area presented like the supplyside procedure in and basically you cannot catch standards that infuriated Beijing that hearing and we shall act summarizes besides J. continues flag the fountains on the and so on because of the size of that they little with standard we with the declassified the course of this year and you might wonder over which kind of signatures this series of formulated when it is formulating them on the air in and there are kind of a topological a construction and in the internal signature of the only category in our case the cutting the city it is a signature which contains the once sought for each object of the and there was no function the more for each Otto and there 1 edition of the monthly chiseled gives the in C so this kind of signature something very useful because it allows them as tool heightened you will instruct the readytowear about the things that had been in your category so the series of events for this particular part this laughter and it is just something here which is useful to know when people say that uh thought was user to behave as a generalized universities of sites away selected especially when you consider the scene a language of all the talk was defined in this way and you can reformulate the many properties that old you have told us that the intensive sequence formulated by using this for my language and we share and we basically you can rule that by using the security conclusion is simple example is the image you want England expertise in 1 or more for than if you when he saddled with it how you like the article in the China will delight that his condition injectivity will divide their method and they data sell using this language as latenight and and you have to sequence and there you can formulate a condition of your model to be of his amazing saying that reduces equipment that uses studies even it's all the little political structure we should constitutes the presiding in interpreting it a signature is on his way so you interpret the results as the corresponding objects to the final singles and singularly worlds users satisfied in being there In total education structure PC and so you see this is just 1 example but of course it is needed ,comma Fuller in general you can override the complicated feelings the American argues it's politically imagining that you are in In a saturated conditions and you and you win and you will be able to say although although things go on you inside your locals as you were working in unison .period because there's a lot of questions student to pay attention to something such as you only have compounded the quantification you are you can refuse a excluded me that all rational choice of missing about provided that you speak with this and what was said and you will know that enabled so this is where there is more the essence of this construction we need to focus on the will at the request of the it will was it was 1 of the
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amendments to agree missing from the where we the Ministry of Communications because yeah I used to work through the roof of his recruiting now on offer for it's a it's very practical OK so now I don't have much more time I would like to just the mentioned that as we had
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defended the actions of this isn't that the categories and we also have this said he did not answer the plant which is a defendant in the ways of building the classic so I gave the system under
1:07:02
construction or bacteria can also an uninformed poker let's just or maybe them from the contagion then you will have led the classifying Tobosa injury isn't it just like that all of the if he is a regular you had an eternity waiting too community J. random and this is called a denial that apology so enthusiastic about apology and defined by saying advance accompanying their CDs 1 that the a call medical bodies in a role that the man is the identity is its suits me fine in this way as it's on the same thing as far as the set of origin at the time so you see we have a genuinely different sides of the conditions for the same at all or some of the school will not coherent then you have and yet will have to find out that type of origin which is called a coherent apologetic on the floor and was inducted camping good this is categorized by fact that there is serious ,comma adding that if and only if it contains a requirement the calling a governing this the sense over the size of this category of what they saw as you can see you see you have already made a major German companies credit categories included in the initial have formerly found ways of dealing with the classified the was because of course will release of the word history of the world this is safety this associates with the little genius because you know you won't need any topology because the apology was becomes essential for regular on the battle for of only needed better define the represents definately meets NBC all you had to go the way thinking because for this hearing you say that you had a fight if I had a condition category and I take advantage of apology I just get custody of when 192 lasers and many sentiment in construction of classifying the wasn't should 90 and will have battered the most dangerous thing to do is a stable history there's a confusion fury because of otherwise you will not end up with a confusion category and with saying that the category that is not confusion knocking some of the more difficult the market was initially developed by the hand the interconnection construction which was not just Florida right here in my for universal all here anyway and OK so and they're just there to conclude that the powerful today I would like to make a just a couple of remarks about the usefulness of having a different sides of the fusion promising so yeah we have seen that that would have been so different will simulate involvement in the classifying Gospels and there is a way to make good use of the system to extract information about mysterious places of interest and move initial requested that the 1 Quebec polls user and the communities there at the very beginning imagine that the police have enough to eat but they decide to consider it as a agreed hear and all I decided to consider it as a dramatic your soul and of course they would have in principle defined the notions of repeated for a sequence that which are regular because only a little faster when I irregular sequence I can also see it as a great and sequence I will have emotional probably the only guy later to this fragments and also rejected these fragmented and of course allegedly strident as well in principle these things will be different and that the fact that they have not done
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and that is a very simple way to CBS that these procedures independence by just comparing these different representations of the classic you know that they're basically going abroad many in the center of the fury in a fragmentary and this something invariant make
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again immediately .period although the demolished the models are clearly same as on the classifying walls will be the same but that it will have to defend their
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presentations and sold the measure for instance that you consider and last year the ball following that logic and lodging so you Naser and then you can exploit the sum to reduce said that there had been 2 motions of probability of missing all you know where you are and also commented that the EU had a universal knowledge all the fury built in there and in a fragment of neurologic anything universal model that began in the language of the Department of coherent village but that the story modern such correspondence which under under this agreement not hold seasonally corresponded to each other under this equipment such as body indicating what we did the same thing as many in India but butler 1 as we're seeing corresponds to probably in the corresponding fragments so yeah we should have a probability you know you have logic and he would have really thinking of coherent logic to see they will be necessary equivalent with each of them because they are connected by this you see it's very easy you don't even need to look at all the rules of inference undefined new alliance soundness of course want to see it certainly seems to want to you have to we
1:14:08
we will have something to do with the ruling it will shares in the conspiracy will exactly exactly exactly what exactly is the best the size of the Nunavut proved to be this is a good example businesses presides at the the
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annual capacity to manage played like that I don't think so that you can see it as see this is just the considering an environment which is the
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notion of universal model this year it from a little different points of view you
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see basically just the right
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here because the past this did you have worry about the activities of the it will be at the site of the of of the I'm fine at because he lives in designing things and he was told and you have to work on all the time you know of course that you can have a say in the center of the sequence of the human rights of their wives would only here and obviously want from their things that this is the year so you to make things that it's not just that and I also don't know who you are and what you want to know something about conditions the in the fragments of both generated by the end of the fact that I like to think about that satisfies the former combatants about misleading data about ability the classical theater and he's certainly not satisfied about but the thing that you have the selectors during which he said was his eyes he was saying that he had a hole in the
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language of your theory and that it the same things even given context that it can you although it possibly even the paraphernalia of coherent form this year there the final
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results said all of the sudden death of these candidates may find that some of the junction of the the season combat on health policy and political argument that it will as follows the head of the agency is this is the sort of thing that has made him 1 of the from the former of Soviet was
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all so when you have a States of this that we were negotiating session to consider my and my fear involved in a
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coherent and logic an angel and encouraging people to exploit the existence of disbelief and representation of Solomon these sentiment have my 2 sites not going at all I know conceded this is invariant I change my mind I consider the notional contract object that doubles a complement of doing so because he's just an object such that there is a recovery Ingleby that contains a fine example of so if I look at this notion so in I started it's something that comes from the side that so and in the sense that this condition it is not a condition that they can formulate this site because even I only had a decent fine archetypes topology so I can help to formulate their but they concluded you are using an Welfel little out of the way I take it I sent you for the unit ended in Seoul and it was held up by a very simple calculations sites that the system is apologies of Hanukkah then the subject is combined it's just that have anything to against being that you can verify so is the geometry his seat on the side of the complies the comparison there are and what you had that of course and this is an invariant so you frustrated him and a leader of the and the sharing of their behind Societe another amazing Conway way to reduce and in this way you can you see this season just lose strength and the fact that the amendment even wasn't variations like these Kennedy got to strikes for waterproofs all results and not be otherwise anyway and I I think that's the style of and so I ordered a twoday had wanted to volunteer about the the latest cheering for some of the abuses of the past rental costs unfortunately ideas for many questions and it couldn't market along with respect with all the things that are going of our interim