# Model theory of satisfaction classes

## Roman Kossak

### The City University of New York

All countable recursively saturated models of Peano Arithmetic have nonstandard satisfaction classes. In fact, each such model has a great variety of nonstandard satisfaction classes. I will survey model theoretic techniques that can be applied to construct many different inductive satisfaction classes, and I will show how, in return, inductive satisfaction classes are used to prove important result about recursively saturated models of PA. I will also pose an open problem concerning a possible converse to Tarski’s undefinability of truth theorem.

Pdf slides for the talk are here: Satisfaction Classes

Roman Kossak is professor of mathematics at The City University of New York, at Bronx Community College and also at the CUNY Graduate Center. He conducts research in mathematical logic, especially in model theory of Peano Arithmetic.