# Sh:447

- Kojman, M., & Shelah, S. (1992).
*The universality spectrum of stable unsuperstable theories*. Ann. Pure Appl. Logic,**58**(1), 57–72. arXiv: math/9201253 DOI: 10.1016/0168-0072(92)90034-W MR: 1169786 -
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. - published version (16p)

Bib entry

@article{Sh:447, author = {Kojman, Menachem and Shelah, Saharon}, title = {{The universality spectrum of stable unsuperstable theories}}, journal = {Ann. Pure Appl. Logic}, fjournal = {Annals of Pure and Applied Logic}, volume = {58}, number = {1}, year = {1992}, pages = {57--72}, issn = {0168-0072}, mrnumber = {1169786}, mrclass = {03C45 (03C55)}, doi = {10.1016/0168-0072(92)90034-W}, note = {\href{https://arxiv.org/abs/math/9201253}{arXiv: math/9201253}}, arxiv_number = {math/9201253} }