Logic Seminar
Fred Drueck
UIC
Vaughtian Pairs, Morasses, and Superlimits
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.
Tuesday March 27, 2012 at 4:00 PM in SEO 427