The universality spectrum of stable unsuperstable theories
Logic
2016-09-06 v1
Abstract
It is shown that if T is stable unsuperstable, and aleph_1< lambda =cf(lambda)< 2^{aleph_0}, or 2^{aleph_0} < mu^+< lambda =cf(lambda)< mu^{aleph_0} then T has no universal model in cardinality lambda, and if e.g. aleph_omega < 2^{aleph_0} then T has no universal model in aleph_omega. These results are generalized to kappa =cf(kappa) < kappa (T) in the place of aleph_0. 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 .
Cite
@article{arxiv.math/9201253,
title = {The universality spectrum of stable unsuperstable theories},
author = {Menachem Kojman and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9201253},
year = {2016}
}