Universal-existential theories of fields

2024/05/21 by Sylvy Anscombe, Arno Fehm, Anscombe, Sylvy +1
Earth and Planetary Sciences · #03C60 #12J20 #12L05 #12L12 #14H05 #Earth Systems and Cosmic Evolution #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.2405.12771

openalex publication_date 2024/05/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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.

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