28 citations · 60 across the 11 of their papers we have counts for
6 papers · 1 filter
Counting mod n in pseudofinite fields
Will Johnson
We show that in an ultraproduct of finite fields, the mod- nonstandard size of definable sets varies definably in families. Moreover, if is any pseudofinite field, then one…
Interpretable sets in dense o-minimal structures
Will Johnson
We give an example of a dense o-minimal structure in which there is a definable quotient that cannot be eliminated, even after naming parameters. Equivalently, there is an interpre…
Dp-finite fields III: inflators and directories
Will Johnson
We develop some tools for analyzing dp-finite fields, including a notion of an ``inflator'' which generalizes the notion of a valuation/specialization on a field. For any field …
Dp-finite fields II: the canonical topology and its relation to henselianity
Will Johnson
We continue our earlier investigation of dp-finite fields. We show that the "heavy sets" of [6] are exactly the sets of full dp-rank. As a consequence, full dp-rank is a definable…
Finite burden in multivalued algebraically closed fields
Will Johnson
We prove that an expansion of an algebraically closed field by arbitrary valuation rings is NTP, and in fact has finite burden. It fails to be NIP, however, unless the va…
Dp-finite fields I: infinitesimals and positive characteristic
Will Johnson
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…