28 citations · 60 across the 11 of their papers we have counts for
5 papers · 2 filters
Dp-finite fields VI: the dp-finite Shelah conjecture
Will Johnson
We prove the dp-finite case of the Shelah conjecture on NIP fields. If K is a dp-finite field, then K admits a non-trivial definable henselian valuation ring, unless K is finite, r…
Dp-finite fields V: topological fields of finite weight
Will Johnson
We prove that unstable dp-finite fields admit definable V-topologies. As a consequence, the henselianity conjecture for dp-finite fields implies the Shelah conjecture for dp-finite…
Dp-finite fields IV: the rank 2 picture
Will Johnson
We investigate fields of characteristic 0 and dp-rank 2. While we do not obtain a classification, we prove that any unstable field of characteristic 0 and dp-rank 2 admits a unique…
Forking and Dividing in Fields with Several Orderings and Valuations
Will Johnson
We consider existentially closed fields with several orderings, valuations, and -valuations. We show that these structures are NTP of finite burden, but usually have the ind…
A criterion for uniform finiteness in the imaginary sorts
Will Johnson
Let be a theory. If eliminates , it need not follow that eliminates , as shown by the example of the -adics. We give a criterion…