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Preprint Number 1588
1588. Will Johnson Partial results on dp-finite fields E-mail: Submission date: 27 March 2019 Abstract: We prove that NIP valued fields of positive characteristic are henselian. Furthermore, we partially generalize the known results on dp-minimal fields to dp-finite fields. We prove a dichotomy: if K is a sufficiently saturated dp-finite expansion of a field, then either K has finite Morley rank or K has a non-trivial Aut(K/A)-invariant valuation ring for a small set A. In the positive characteristic case, we can even demand that the valuation ring is henselian. Using this, we classify the positive characteristic dp-finite pure fields. Mathematics Subject Classification: 03C45 Keywords and phrases: |
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