**Model Theory Seminar**

**Sebastien Vasey (joint work with Will Boney)**

**CMU**

**Title: ** Chains of saturated models in Abstract Elementary Classes, Part 1

**Abstract: **Fix a first-order theory $T$ and a cardinal $\lambda > |T|$. Is the union of a chain of $\lambda$-saturated models of $T$ $\lambda$-saturated? By a classical result of Saharon Shelah, the answer is positive when $T$ is superstable. When $T$ is only stable, this also holds provided that the length of the chain has cofinality at least $|T|^+$. In both cases, the proofs depend on the heavy machinery of forking and averages.

**Date:**Monday, February 2, 2015

**Time: **5:00 – 6:30 PM

**Location: **Wean 8220

**Model Theory Seminar**

**Sebastien Vasey (joint work with Will Boney)**

**CMU**

**Title: ** Chains of saturated models in Abstract Elementary Classes, Part 2

**Abstract: **Fix a first-order theory $T$ and a cardinal $\lambda > |T|$. Is the union of a chain of $\lambda$-saturated models of $T$ $\lambda$-saturated? By a classical result of Saharon Shelah, the answer is positive when $T$ is superstable. When $T$ is only stable, this also holds provided that the length of the chain has cofinality at least $|T|^+$. In both cases, the proofs depend on the heavy machinery of forking and averages.

**Date:**Monday, February 9, 2015

**Time: **5:00 – 6:30 PM

**Location: **Wean 8220