Wednesday, March 30, 20166:15 pmModels of PAGC 4214-03

# Automorphism Groups of Models of Different Theories (Part I)

## Erez Shochat

### St. Francis College

Jim Schmerl recently proved that there are continuum many theories extending PA, for which whenever M and N are countable arithmetically saturated models of two different such theories, their automorphism groups are non isomorphic. In part I, we give a survey of results concerning automorphism groups of countable arithmetically saturated models of PA, and introduce notions and prove results which will be used in part II to prove Schmerl’s Theorem.