Roman Kossak, CUNY
Automorphisms, Jónsson Models, and Satisfaction Classes
25 years ago I wrote a paper on four open problems concerning recursively saturated models of PA. The problems are still open. I will talk about two of them: (1) Let M be a countable recursively saturated model of PA. Can every automorphism of M be extended to some recursively saturated elementary end extension of M? (2) Is there a recursively saturated model of PA that has no recursively saturated elementary submodel of the same cardinality as the model? I will present some partial results involving partial inductive satisfaction classes.