Modal theory of the category of sets

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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