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Universal-existential theories of fields
Published online by Cambridge University Press: 03 September 2025
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)
MSC classification
Primary:
03C60: Model-theoretic algebra
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- Research Article
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- © The Author(s), 2025. Published by Cambridge University Press on behalf of The Edinburgh Mathematical Society.
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