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 $\lambda$.
• Version 1996-03-19_10 (25p) published version (16p)

@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}
}