Universal-existential theories of fields
arXiv:2405.12771 · doi:10.1017/S0013091525100771
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.
Published in Proceedings of the Edinburgh Mathematical Society. This updated version contains a simplified proof of Proposition 5.13