Study analyzes the interaction between first-order field theories and universal-existential fragments, revealing connections between fields.
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)
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Anscombe et al. (2025) studied this question.
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