Distality in valued fields and related structures

Aschenbrenner, Matthias; Chernikov, Artem; Gehret, Allen; Ziegler, Martin

doi:10.1090/tran/8661

Distality in valued fields and related structures
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by Matthias Aschenbrenner, Artem Chernikov, Allen Gehret and Martin Ziegler PDF

Trans. Amer. Math. Soc. 375 (2022), 4641-4710 Request permission

Abstract:

We investigate distality and existence of distal expansions in valued fields and related structures. In particular, we characterize distality in a large class of ordered abelian groups, provide an Ax-Kochen-Eršov-style characterization for henselian valued fields, and demonstrate that certain expansions of fields, e.g., the differential field of logarithmic-exponential transseries, are distal. As a new tool for analyzing valued fields we employ a relative quantifier elimination for pure short exact sequences of abelian groups.

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