Department of         Mathematical Sciences Events People Colloquia and Seminars Conferences Centers Positions Areas of Research About the Department Alumni Model Theory Seminar Will Boney Carnegie Mellon University Title: Categoricity in $L_{\kappa, \omega}$ when $\kappa$ is strongly compact, Part 2. 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 22, 2010Time: 5:00 pmLocation: Wean Hall 7201Submitted by:  Rami Grossberg