English

Ultrafilter extensions do not preserve elementary equivalence

Logic 2019-11-05 v2

Abstract

We show that there exist models M1\mathcal M_1 and M2\mathcal M_2 such that M1\mathcal M_1 elementarily embeds into M2\mathcal M_2 but their ultrafilter extensions β(M1)\beta(\mathcal M_1) and β(M2)\beta(\mathcal M_2) are not elementarily equivalent.

Keywords

Cite

@article{arxiv.1712.06198,
  title  = {Ultrafilter extensions do not preserve elementary equivalence},
  author = {Denis I. Saveliev and Saharon Shelah},
  journal= {arXiv preprint arXiv:1712.06198},
  year   = {2019}
}
R2 v1 2026-06-22T23:20:55.108Z