Ernest Schimmerling

Mathematical logic seminar - December 1, 2005

Time: 12 - 1:20 p.m.

Room: OSC 201

Speaker: Spas Bojanov
Department of Mathematical Sciences
Carnegie Mellon University

Title: On a paper by Makkai and Shelah

Abstract:     An outline of the following theorem will be presented:

Assume κ is a strongly compact cardinal, T is a theory in a fragment F of Lκω over a language L, and κ' = max(κ,|F|). Assume T is categorical in λ. If λ is a successor cardinal and λ > ((κ') < κ )+, then T is categorical in every cardinal ≥ min(λ,BETH(2κ' )+).

This is one of the main results from the 1990 paper by Makkai and Shelah, "Categoricity of theories in Lκω, with κ a compact cardinal". This result should be considered a step towards settling Shelah's categoricity conjecture for Lω1ω, which says the following.

Given a countable language L and T a theory in Lω1ω, if T is categorical in λ>BETHω1, then T is categorical in every cardinal ≥BETHω1.