Sylvy Anscombe, Arno Fehm
Published 2024-05-21Version 1
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.
Krull dimension of types in a class of first-order theories
Axiomatizing the existential theory of Fp((t))
A remark about amalgamation of union of theories
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