Will Boney: Large Cardinal Axioms from Tameness in AECs

Date: Monday, March 23, 2015

Time: 5:00 – 6:30 PM
Location: Wean 8220

Model Theory Seminar

Will Boney,  UIC

Title:   Large Cardinal Axioms from Tameness in AECs.

Abstract:   It was recently shown that various locality properties for Galois types hold globally in the presence of large cardinals.  The natural question became whether these locality properties could consistently hold at small cardinals.  Surprisingly, this turns out not to be the case.  In joint work with Spencer Unger, we generalize an example of Shelah to show that the various global locality properties imply and (therefore) are equivalent to the appropriate large cardinals.  As an application to category theory, we show that a theorem of Makkai and Pare on accessible categories has large cardinal strength.

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