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.