Abstract
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 some small set A. In the positive characteristic case, we can even obtain a henselian valuation ring. Using this, we classify the positive characteristic dp-finite pure fields.
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