Submission date: 21 May 2024

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.

Mathematics Subject Classification: 03C60, 12L05, 12L12, 12J20, 14H05

Keywords and phrases:

Full text arXiv 2405.12771: pdf, ps.