Choice, Groups, and Topoi

15.04.2021 15:00 - 16:30

Andreas Blass (University of Michigan)

Work of Tarski, Mostowski, Gauntt, and Truss provides finite, group-theoretic criteria for ZF-provability of implications between weak choice axioms of the form "every family of n-element sets has a choice function" or "every countable family of n-element sets has a choice function."  From a sufficiently broad, category-theoretic viewpoint, these implications and the equivalent group-theoretic criteria look like exactly the same statements but interpreted in different categories, namely certain particular sorts of topoi. The main result is that this equivalence applies not only to these particular sorts of topoi but to all topoi. I plan to describe the ingredients of this work — choice principles, group properties, and topoi — and, if time permits, give a hint about the ideas in the proofs.



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