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