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Model Theory Seminar
William Boney
Carnegie Mellon University
Title: Categoricity in $L_{kappa, omega}$ when $kappa$ is strongly compact

Abstract: In this series of talks, I will present a result of Shelah and Makkai that is an analogue to Morley's theorem in $L_{\kappa, \omega}$. This requires using $\kappa$ being strongly compact, which says that any collection of sentences from $L_{\kappa, \kappa}$ is consistent iff every $< \kappa$ sized subset of it is consistent. The proof of this is much different than the proof of Morley's theorem and goes through a concept called 'forking,' which is an important extension of splitting.

The first talk will introduce the theorems to be proved and will begin to prove some of the basic properties of $L_{\kappa, \omega}$ when $\kappa$ is super compact, leading up to the amalgamation property.

Date: Wednesday, September 15, 2010
Time: 5:00 pm
Location: Wean Hall 7201
Submitted by:  Rami Grossberg