## Logic and topology

Video in TIB AV-Portal: Logic and topology

 Title Logic and topology Title of Series Topos à l'IHES Part Number 17 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 10.5446/20758 (DOI) Publisher Release Date 2015 Language English

 Subject Area Mathematics Abstract The logic of topos is naturally described using intuitionistic higher-order logic, an intuitionistic version of a simple theory of types, a formal system designed by A. Church (1940). Two important axioms of this formal system are the axiom of extensionality and the axiom of description. Recently, Voevodsky formulated the axiom of univalence, which can be seen as a natural generalization of the axiom of extensionality, and showed that this axiom is valid in a model where a type is interpreted as a Kan simplicial set. This model uses classical logic in an essential way. We present a variation of this model which is carried out in an intuitionistic meta-theory and explain how the axiom of description is validated in this model.
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Functional (mathematics) Existence Transportation theory (mathematics) State of matter Multiplication sign Modulform Sheaf (mathematics) Propositional formula Student's t-test Cartesian product Frequency Goodness of fit Mathematics Positional notation Meeting/Interview Natural number Operator (mathematics) Analogy Ring (mathematics) Logic Modulform Antiderivative Extension (kinesiology) Fiber (mathematics) Position operator Curve fitting Set theory Physical system Area Sine Moment (mathematics) Propositional formula Algebraic structure Basis <Mathematik> Limit (category theory) Element (mathematics) Numerical analysis Connected space Computer animation Logic Theorem Set theory Game theory Arithmetic progression Family
Complex (psychology) Presentation of a group Euler angles State of matter Logarithm Multiplication sign 1 (number) Sheaf (mathematics) Kontraktion <Mathematik> Propositional formula Axiom Mereology Total S.A. Mathematical structure Vibration Grothendieck topology Explosion Duality (mathematics) Mathematics Positional notation Different (Kate Ryan album) Military operation Logic Universe (mathematics) Extension (kinesiology) Fiber (mathematics) Descriptive statistics Position operator Physical system Area Logical constant Process (computing) Point (geometry) Propositional formula Special unitary group Nominal number Lattice (order) Element (mathematics) Higher-order logic Connected space Proof theory Category of being Uniformer Raum Phase transition Theorem Mathematician Resultant Directed graph Spacetime Point (geometry) Suspension (chemistry) Expression Functional (mathematics) Flock (web browser) Sequel Divisor Observational study Connectivity (graph theory) Paradox Student's t-test Inequality (mathematics) Rule of inference Event horizon Product (business) Frequency Formal power series Operator (mathematics) Modulform Liquid Analytic continuation Summierbarkeit Set theory Condition number Standard deviation Multiplication Sine Projective plane Physical law Content (media) Mathematical analysis Algebraic structure Density of states Binary file Equivalence relation Inclusion map Formal power series Computer animation Logic Function (mathematics) Factory (trading post) Network topology Universe (mathematics) Family Maß <Mathematik>
Complex (psychology) Group action Presentation of a group Logarithm Water vapor Open set Solid geometry Vibration Expected value Insertion loss 5 (number) Descriptive statistics Physical system Uniform convergence Mass Maxima and minima Lattice (order) Sequence Category of being Intuitionistische Logik IRIS-T Mathematical singularity Theorem Arithmetic progression Spacetime Directed graph Point (geometry) Free group Student's t-test Infinity Element (mathematics) Frequency Latent heat Goodness of fit Finite set Helmholtz decomposition Energy level Modulform Directed set Standard deviation Model theory Commutator Operator (mathematics) Basis <Mathematik> Line (geometry) Equivalence relation Formal power series Set theory Musical ensemble Game theory Building Euler angles State of matter Multiplication sign Decision theory Sheaf (mathematics) Propositional formula Insertion loss Parameter (computer programming) Meeting/Interview Position operator Fiber (mathematics) Stability theory Area Process (computing) Closed set Moment (mathematics) Distributive property Computability Hypothesis Connected space Proof theory Funktor Uniformer Raum Normal (geometry) Fundamental theorem of algebra Existence Functional (mathematics) Divisor Modulform Tube (container) Distance Discrete element method Formal power series Causality Operator (mathematics) Euler's formula Free group Set theory Condition number Sine Forcing (mathematics) Projective plane Incidence algebra Numerical analysis Algebra Factory (trading post) Object (grammar) Marginal distribution Maß <Mathematik>
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