Andrew Coppola : Equicardinality quantifiers in Abstract Elementary Classes

Posted by Matthias Aschenbrenner , part of the Logic Seminar.

At

Nov. 10, 2005, 2 p.m.

In

SEO 427

Abstract

We consider theories in logics equipped with the generalized quantifier that asks, "do there exist |M|- many". The goal is to study these within the framework of Abstract Elementary Classes. However, they are slightly more general as they do not satisfy the full axiomatic chain conditions on substructures. One target is a variant of the Los Conjecture for these classes. This reconciles results approached from very different directions. Lawskoski and Pillay prove the Los Conjecture for the class of Gross Models (models of a complete first-order theory where all infinite definable sets have cardinality equal to the model). This can be recast in the work on tame AECs, initiated by Grossberg and Vandieren.

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