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Model Theory Seminar
Daniel Rodriguez
Carnegie Mellon University
Title: Theorem for uncountable first-order theories. Part 5

Abstract: This sequence of lectures will be dedicated to the proof of the following theorem: If T is categorical in some a cardinal >|T| then T is categorical in all cardinals >|T|.

The first proof (discovered by Shelah) took an entire year to present using the full power of forking and orthogonality calculus. We will see a simpler second proof (also due to Shelah), inspired by some ideas from the Baldwin-Lachlan proof of Morley's categoricity theorem combined with elementary facts from super stability.

In the first 3 lectures it was established that categoricity in a cardinal >|T| implies that every model of card >|T| is locally saturated, Deg[x=x] is bounded and every infinite definable set contains a weakly-mnimal set.

Date: Monday, April 16, 2012
Time: 5:00 pm
Location: Wean Hall 8220
Submitted by:  Grossberg