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Universal-existential theories of fields

Part of: Topological fields Connections with logic Model theory Curves

Published online by Cambridge University Press:  03 September 2025

Sylvy Anscombe Open the ORCID record for Sylvy Anscombe [Opens in a new window]  and
Arno Fehm Open the ORCID record for Arno Fehm [Opens in a new window]
Sylvy Anscombe*
Affiliation:
Université Paris Cité and Sorbonne Université, CNRS, IMJ-PRG, Paris, France
Arno Fehm
Affiliation:
Institut für Algebra, Technische Universität Dresden, Dresden, Germany
*
Corresponding author: Sylvy Anscombe, email: sylvy.anscombe@imj-prg.fr
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Abstract

We study 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.

Dedicated to the memory of Alexander Prestel (1941–2024)

Keywords

Model theoryfieldsvalued fieldsfunction fieldshenselianity

MSC classification

Primary: 03C60: Model-theoretic algebra
Secondary: 12L05: Decidability 12L12: Model theory 12J20: General valuation theory 14H05: Algebraic functions; function fields

Information

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 69 , Issue 1 , February 2026 , pp. 95 - 124
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of The Edinburgh Mathematical Society.

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