# Sh:877

• Shelah, S. (2014). Dependent T and existence of limit models. Tbilisi Math. J., 7(1), 99–128.
• Abstract:
We continue [Sh:868] and [Sh:783]. The problem there is when does (first order) T have a model M of cardinality \lambda which is (one of the variants of) a limit model for cofinality \kappa, and the most natural case to try is \lambda=\lambda^{< \lambda}>\kappa={\rm cf}(\kappa)>|T|. The stable theories has one; are there unstable T whnce of limit models AUTHORS: Saharon Shelah ich has such limit models? We find one: the theory T_{\rm ord} of dense linear orders. So does this hold for all unstable T? As T_{\rm ord} is prototypical of dependent theories, it is natural to look for independent theories. A strong, explicit version of T being independent is having the strong independence property. We prove that for such T there are no limit models. We work harder to prove this for every dependent T, i.e., with the independence property though a weaker version. This makes us conjecture that any dependent T has such models. Toward this end we continue the investigation of types for dependent T.
• Version 2015-06-02_12 (28p) published version (30p)
Bib entry
@article{Sh:877,
author = {Shelah, Saharon},
title = {{Dependent $T$ and existence of limit models}},
journal = {Tbilisi Math. J.},
fjournal = {Tbilisi Mathematical Journal},
volume = {7},
number = {1},
year = {2014},
pages = {99--128},
issn = {1875-158X},
mrnumber = {3313049},
mrclass = {03C45 (03C50 03C55 06A05)},
doi = {10.2478/tmj-2014-0010},
note = {\href{https://arxiv.org/abs/math/0609636}{arXiv: math/0609636}},
arxiv_number = {math/0609636}
}