English

Non-definability of rings of integers in most algebraic fields

Logic 2021-10-15 v2 Number Theory

Abstract

We show that the set of algebraic extensions FF of Q\mathbb{Q} in which Z\mathbb{Z} or the ring of integers OF\mathcal{O}_F are definable is meager in the set of all algebraic extensions.

Keywords

Cite

@article{arxiv.2011.14367,
  title  = {Non-definability of rings of integers in most algebraic fields},
  author = {Philip Dittmann and Arno Fehm},
  journal= {arXiv preprint arXiv:2011.14367},
  year   = {2021}
}

Comments

Added some remarks. Accepted for publication in the Notre Dame Journal of Formal Logic