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Is the Continuum Hypothesis a definite mathematical problem?


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Title Is the Continuum Hypothesis a definite mathematical problem?
Title of Series Paul Bernays Lectures 2012
Number of Parts 4
Author Feferman, Solomon
License CC Attribution - NonCommercial - NoDerivatives 2.5 Switzerland:
You are free to use, copy, distribute and transmit the work or content in unchanged form for any legal and non-commercial purpose as long as the work is attributed to the author in the manner specified by the author or licensor.
DOI 10.5446/36704
Publisher Eidgenössische Technische Hochschule (ETH) Zürich
Release Date 2012
Language English

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Subject Area Mathematics
Abstract Georg Cantor established the modern theory of sets with his theory of transfinite cardinal and ordinal numbers, which began with his proof that the set of real numbers has greater cardinality than the set of natural numbers; Cantor’s Continuum Hypothesis (CH) states that there is no intermediate cardinal number. The call to establish CH was the first in the famous list of twenty-three challenging mathematical problems that Hilbert posed at the International Congress of Mathematicians in 1900. Yet, a century later, it did not appear on the list of the seven Millennium Prize Problems worth a million dollars each, despite the fact that no solution to it has been found in the mean time. In this lecture I will discuss the evidence for my view (contrary to Gödel above all) that CH is not a definite mathematical problem, despite the fact that it is formulated in terms of concepts that have become an established part of mathematics.

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