Modal theory of the category of sets

Posted on by Wojciech Aleksander Wołoszyn

This was a talk for the Junior Logic Seminar at the University of Oxford, 7th of June 2022.

Abstract. I shall investigate the modal theories and validities in a variety of cases arising from the archetypical concrete category of sets and functions. I introduce new insights into the method of control statements, answering a MathOverflow question about buttons and switches.

The MathOverflow question I am referencing is Are buttons really enough to bound validities by S4.2?

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Published by Wojciech Aleksander Wołoszyn

I am a DPhil student in Mathematics at the University of Oxford. My academic interests revolve around the philosophy of foundations of mathematics in the context of V and the multiverse debate. Currently, I am mostly preoccupied with research on modal model theory - an emerging field in mathematical logic. My academic advisers are Professor Joel David Hamkins (University of Notre Dame), Professor Ehud Hrushovski, and Professor W. Hugh Woodin (Harvard University). Previously, I was a Recognised Student in Philosophy at the University of Oxford, under Professor Hamkins's supervision.