Fred Drueck : Vaughtian Pairs, Morasses, and Superlimits

Posted by , part of the Logic Seminar.

At

March 27, 2012, 4 p.m.

In

SEO 427

Abstract

We recall a theorem of Lessmann about producing two-cardinal models based off the existence of a Vaughtian pair for an AEC stable in $\aleph_0$ and discuss combinatorial difficulties to extending this result to AECs with uncountable Löwenheim number. We give an abstract framework for proving this result, which is an analog of Vaught's Two Cardinal Theorem for AECs, which we call a ``superlimit'' and contrast this with Shelah's definition of ``superlimit''. We discuss also the difference between unions of limit models being limit models and limit models being unique up to isomorphism and discuss the possibility using Morasses to prove an analog of Chang's gap-2 transfer theorem for AECs.