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 L_{κω} 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 L_{κω}, with κ a compact cardinal". This result should be considered a step towards settling Shelah's categoricity conjecture for L_{ω1ω}, which says the following. Given a countable language L and T a theory in L_{ω1ω}, if T is categorical in λ>BETH_{ω1}, then T is categorical in every cardinal ≥BETH_{ω1}.
