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C-minimal fields have the exchange property

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arxiv 2403.17478 v2 pith:RMDEB46O submitted 2024-03-26 math.LO

Will Johnson This is my paper · ORCID
classification math.LO
keywords c-minimalfieldsboundednessexchangefieldpolynomialpropertyresidue
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We show that C-minimal fields (i.e., C-minimal expansions of ACVF) have the exchange property, answering a question of Haskell and Macpherson. Additionally, we strengthen some theorems of Cubides Kovacsics and Delon on C-minimal fields. First, we show that definably complete C-minimal fields of characteristic 0 have generic differentiability. Second, we show that if the induced structure on the residue field is a pure ACF, then polynomial boundedness holds. In fact, polynomial boundedness can only fail if there are unexpected definable automorphisms of the multiplicative group of the residue field.

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  1. On definable groups in dp-minimal topological fields equipped with a generic derivation

    math.LO 2025-05 accept novelty 6.0 of 10

    In dp-minimal topological fields of characteristic 0 with a generic derivation, every finite-dimensional definable group densely embeds in a definable group of the underlying field, and in a definable D-group under a ...

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