English

Dependent T and existence of limit models

Logic 2017-08-08 v3

Abstract

Does the class of linear orders have (one of the variants of) the so called (lambda, kappa)-limit model? It is necessarily unique, and naturally assuming some instances of G.C.H. we get some positive, i.e. existence results. More generally, letting T be a complete first order theory and for simplicity assume G.C.H., for regular lambda > kappa > |T| does T have (variants of) a (lambda,kappa)-limit models, except for stable T? For some, yes, the theory of dense linear order, for some, no. Moreover, for independent T we get negative, i.e. non-existence results. We deal more with linear orders.

Keywords

Cite

@article{arxiv.math/0609636,
  title  = {Dependent T and existence of limit models},
  author = {Saharon Shelah},
  journal= {arXiv preprint arXiv:math/0609636},
  year   = {2017}
}
R2 v1 2026-07-22T17:42:51.575Z