The universality spectrum of stable unsuperstable theories
Menachem Kojman, Saharon Shelah
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 .
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