Fall 2017

CUNY Graduate Center
Room 6495
Wednesdays 5:15-6:45pm
Organized by Alf Dolich and and Kameryn Williams

September 6
Alf Dolich, CUNY
On Computable Axiomatizability of Elementary Classes
I will discuss work of Peter Sinclair which provides a general mechanism for showing that an elementary class is not computably axiomatizable. The proof involves an interesting use of models of arithmetic.

September 13
Athar Abdul-Quader, CUNY
Dolich sets
We say an undefinable subset X of a model M is “Dolich” if the dcl relation in M coincides with the dcl relation in (M, X). In this talk, I will explore a few preliminary results on the existence and non-existence of Dolich sets. First we will see that recursively saturated models have no inductive Dolich subsets. On the other hand, we will then see that any cofinal extension of a prime model of PA has inductive Dolich subsets. I will then weaken this notion and talk about what we know about the existence of these “weaker” Dolich sets.

September 27
Alf Dolich, CUNY
When are order isomorphic models of PA isomorphic?
I will revisit Shelah’s paper “Models of PA: when two elements are necessarily order automorphic”. In this paper Shelah begins to consider to what extent the order type of a model of PA determines its isomorphism type.