MSc Mathematics Pre-thesis Seminar
Speaker: Ujjwal Kiran Das
Date: Friday, November 3, 2023
Time: 10.30 - 11.30 AM
Venue: Lecture Hall 202
Morley's Proof of the Categoricity Theorem and a Generalization by Shelah
Ujjwal Kiran Das
Chennai Mathematical Institute.
03-11-23

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Abstract

Proved by Michael Morley in 1965, the Categoricity Theorem is one of the most well-known results in model theory and states that a complete theory over a countable language is categorical in one uncountable cardinality iff it is categorical in all of them. Morley's proof of this result connects a wide range of ideas, including an ingenious adaptation of the usual analysis of Cantor-Bendixson derivatives over a compact Hausdorff space.

We will take a close look at these ideas and also look at a brief sketch of Saharon Shelah's proof, generalizing the above theorem to complete theories over languages of any infinite cardinality.