Matthias Aschenbrenner, Artem Chernikov, Allen Gehret, Martin Ziegler
Published 2020-08-22Version 1
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 AKE-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.
Transfer principles for forking and dividing in expansions of pure short exact sequences of Abelian groups
The domination monoid in henselian valued fields
Model completeness for the differential field of transseries with exponentiation
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