James Cummings and Will Boney

Model Theory Seminar, Monday  September 10
Time: 5:00 pm
Location: Wean 8220

Will Boney
Carnegie Mellon University
Title: Tameness and Large Cardinals, part 1

Abstract: Tameness is a property of Abstract Elementary Classes isolated by Grossberg and Van Dieren that has proved very useful, especially in proving Shelah’s Categoricity Conjecture. In these talks, we show that large amounts of tameness follow directly from different large cardinals, specifically strongly compact, measureable, and weakly compact. We will present a variety of proofs, showcasing how different large cardinal properties (ultrafilters, elementary embeddings, and indescribability) can be used model theoretically.



Mathematical logic seminar – September 11 2012
Time:     12:00 – 13:20
Room:     Wean Hall 7201

Speaker:         James Cummings
Department of Mathematical Sciences
Carnegie Mellon University

Title:     Intermediate models


This is the second in a series of talks whose goal is to describe and check a scenario for a proof of the following theorem: if c is Cohen-generic over L,  then  there is a transitive class model M of ZF intermediate between L and L[c] which is not of the form L(A) for any A.

I will start by reviewing the key material from last week.

This scenario is due primarily to Hugh Woodin, with contributions by
Andrew Brooke-Taylor,  James Cummings , Moti Gitik, Menachem Magidor, Ralf Schindler, and Philip Welch.

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