The universality spectrum of stable unsuperstable theories
Abstract
It is shown that if T is stable unsuperstable, and aleph1< lambda =cf(lambda)< 2aleph0, or 2aleph0 < mu+< lambda =cf(lambda)< mualeph0 then T has no universal model in cardinality lambda, and if e.g. alephomega < 2aleph0 then T has no universal model in alephomega. These results are generalized to kappa =cf(kappa) < kappa (T) in the place of aleph0. Also: if there is a universal model in lambda >|T|, T stable and kappa < kappa (T) then there is a universal tree of height kappa +1 in cardinality lambda .
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.