Logic Seminar
John Baldwin
UIC
Category theory and Model Theory: Symbiotic Scaffolds
Abstract: A scaffold for mathematics includes both local foundations for various areas of
mathematics and productive guidance in how to unify them. In a scaffold the unification does not take place by a common axiomatic basis but consists of a systematic
ways of connecting results and proofs in various areas of mathematics. Two scaffolds, model theory and category theory, provide local foundations for many areas
of mathematic including two flavors (material and structural) of set theory and
different approaches to unification. We will discuss salient features of the two scaffolds including their contrasting but bi-interpretable set theories. We focus on the
contrasting treatments of ‘size’ in each scaffold and the advantages/disadvantages
of each for different problems.
Tuesday April 12, 2022 at 4:00 PM in 636 SEO