English

Models of expansions of N with no end extensions

Logic 2010-06-08 v2

Abstract

We deal with models of Peano arithmetic (specifically with a question of Ali Enayat). The methods are from creature forcing. We find an expansion of N such that its theory has models with no (elementary) end extensions. In fact there is a Borel uncountable set of subsets of N such that expanding N by any uncountably many of them suffice. Also we find arithmetically closed A with no definably closed ultrafilter on it.

Keywords

Cite

@article{arxiv.0808.2960,
  title  = {Models of expansions of N with no end extensions},
  author = {Saharon Shelah},
  journal= {arXiv preprint arXiv:0808.2960},
  year   = {2010}
}