University of Birmingham > Talks@bham > Midlands Logic Seminar > Set theoretic principles required for categoricity

Set theoretic principles required for categoricity

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Dedekind proved that two structures satisfying the second order axioms for natural numbers are canonically isomorphic. Obviously a key point in the argument is that, assuming two such structures are not isomorphic, an inductive set must be constructed in one structure that is not the whole thing. Thus set theoretic principles are required for categoricity results of this kind, and these arguments are sensitive to the set theoretic framework we are working in, and in particular what set existence axioms are available.

So the question is, which set existence axioms are actually needed? Simpson and Yokoyama investigated this question. We shall give a reading of their paper, and this will be a useful introduction to some of the methods and results in so-called “reverse mathematics”.

This talk is part of the Midlands Logic Seminar series.

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