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arXiv · 2405.12771

Universal-existential theories of fields

Sylvy Anscombe·Arno Fehm
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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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Sylvy Anscombe, Arno Fehm. 2024-05-21. Universal-existential theories of fields. https://doi.org/10.1017/s0013091525100771

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