Ryan Carpenter : Modal Model Theory: A Potential Foundation for Mathematics?

Posted by Ryan Carpenter , part of the Louise Hay Logic Seminar.

At

March 6, 2023, 4 p.m.

In

612 SEO

Abstract

In this talk, I will introduce the system of modal model theory, an augmented style of first-order logic with remarkable expressive power and desirable model-theoretic properties. We will focus on one particular system of modal model theory: modal graph theory. As it turns out, modal graph theory interprets a very large portion of set-theoretic truth; we investigate whether modal graph theory can interpret full set-theoretic truth, and therefore whether it may serve as the foundation for mathematics.