English

Exact saturation in simple and NIP theories

Logic 2015-10-12 v1

Abstract

A theory TT is said to have exact saturation at a singular cardinal κ\kappa if it has a κ\kappa-saturated model which is not κ+\kappa^{+}-saturated. We show, under some set-theoretic assumptions, that any simple theory has exact saturation. Also, an NIP theory has exact saturation if and only if it is not distal. This gives a new characterization of distality.

Keywords

Cite

@article{arxiv.1510.02741,
  title  = {Exact saturation in simple and NIP theories},
  author = {Itay Kaplan and Saharon Shelah and Pierre Simon},
  journal= {arXiv preprint arXiv:1510.02741},
  year   = {2015}
}
R2 v1 2026-06-22T11:16:44.608Z