Speaker
Tomáš Jakl, Czech Academy of Sciences and Czech Technical University
Title
A Synthetic Road to Locality Theorems
Abstract
In this talk, we give an overview of synthetic results in the game comonad programme and motivate looking into locality theorems. This amounts to taking the minimalistic categorical approach and identifying the crucial categorical structures that make various different results work.
As a first hurdle on the way to locality theorems, we discuss preservation theorems for formulas with free variables, i.e. preservation of types. This is an extension of the composition methods presented by Dan Marsden earlier on. We then further extend this work to the preservation of local formulas and also basic local formulas. Finally, we discuss some categorical components of both Gaifman and Hanf locality theorems.
Slides
A Synthetic Road to Locality Theorems
