**Model Theory Seminar**

**Sebastien Vasey**

**Carnegie Mellon**

**Title: ** Infinitary stability theory, part I

**Abstract: **In 1990, Makkai and Shelah studied the class of models of an $L_{\kappa, \omega}$ sentence, where $\kappa$ is strongly compact. Among many other results, they showed that Galois types (a purely semantic notion of types) and syntactic types conveyed the same information. In particular, Galois types are determined by their restrictions to sets of size less than $\kappa$. This last property was later isolated by Grossberg and VanDieren and called tameness. In this talk, I will show that tameness already implies that Galois types are (in some sense) syntactic, thus generalizing Makkai and Shelah’s result. I will give several applications to the stability theory of tame abstract elementary classes.

**Date:**Monday, October 13, 2014

**Time: **5:00 – 6:30 PM

**Location: **Wean 8220

**Model Theory Seminar**

**Sebastien Vasey**

**Carnegie Mellon**

**Title: ** Infinitary stability theory, part II

**Abstract: **In 1990, Makkai and Shelah studied the class of models of an $L_{\kappa, \omega}$ sentence, where $\kappa$ is strongly compact. Among many other results, they showed that Galois types (a purely semantic notion of types) and syntactic types conveyed the same information. In particular, Galois types are determined by their restrictions to sets of size less than $\kappa$. This last property was later isolated by Grossberg and VanDieren and called tameness. In this talk, I will show that tameness already implies that Galois types are (in some sense) syntactic, thus generalizing Makkai and Shelah’s result. I will give several applications to the stability theory of tame abstract elementary classes.

**Date:**Monday, October 20, 2014

**Time: **5:00 – 6:30 PM

**Location: **Wean 8220

**Model Theory Seminar**

**Sebastien Vasey**

**Carnegie Mellon**

**Title: ** Infinitary stability theory, part III

**Abstract: **In 1990, Makkai and Shelah studied the class of models of an $L_{\kappa, \omega}$ sentence, where $\kappa$ is strongly compact. Among many other results, they showed that Galois types (a purely semantic notion of types) and syntactic types conveyed the same information. In particular, Galois types are determined by their restrictions to sets of size less than $\kappa$. This last property was later isolated by Grossberg and VanDieren and called tameness. In this talk, I will show that tameness already implies that Galois types are (in some sense) syntactic, thus generalizing Makkai and Shelah’s result. I will give several applications to the stability theory of tame abstract elementary classes.

**Date:**Monday, October 27, 2014

**Time: **5:00 – 6:30 PM

**Location: **Wean 8220