# Daniel Rodriguez: Categoricity Theorem for uncountable first-order theories

MONDAY, March 19, 2012

5:00-6:30PM, WeH 822

CMU MODEL THEORY SEMINAR:

Speaker: Daniel Rodriguez

TITLE: Categoricity Theorem for uncountable first-order theories. Part 1

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 ideas from the Baldwin-Lachlan proof of Morley’s categoricity theorem combined with elementary facts from super stability and two-cardinal transfer theorems.