Logic Seminar
Andrew Coppola
UIC
Equicardinality quantifiers in Abstract Elementary Classes
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.
Note the unusal time and day.
Thursday November 10, 2005 at 2:00 PM in SEO 427