# Sh:877

- Shelah, S. (2014).
*Dependent T and existence of limit models*. Tbilisi Math. J.,**7**(1), 99–128. arXiv: math/0609636 DOI: 10.2478/tmj-2014-0010 MR: 3313049 -
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} }