English

Universal-existential theories of fields

Logic 2026-02-04 v4

Abstract

We study various universal-existential fragments of first-order theories of fields, in particular of function fields and of equicharacteristic henselian valued fields. For example we discuss to what extent the theory of a field k determines the universal-existential theories of the rational function field over k and of the field of Laurent series over k, and we find various many-one reductions between such fragments.

Keywords

Cite

@article{arxiv.2405.12771,
  title  = {Universal-existential theories of fields},
  author = {Sylvy Anscombe and Arno Fehm},
  journal= {arXiv preprint arXiv:2405.12771},
  year   = {2026}
}

Comments

Published in Proceedings of the Edinburgh Mathematical Society. This updated version contains a simplified proof of Proposition 5.13

R2 v1 2026-06-28T16:34:17.221Z