4 citations · 5 across the 10 of their papers we have counts for
10 papers · 1 filter
Topologically 1-based T-minimal Structures
Benjamin Castle, Assaf Hasson, Will Johnson
We prove group existence and structure theorems in a general setting of tame topological theories. More precisely, we identify a linear/non-linear dividing line -- called topologic…
Largeness and generalized t-henselianity
Will Johnson
Let be a countable field. Then is large in the sense of Pop if and only if it admits a field topology which is "generalized t-henselian" (gt-henselian) in the sense of Ditt…
Large implies henselian
Will Johnson, Chieu-Minh Tran, Erik Walsberg +1
Fix a field . We show that is large if and only if some elementary extension of is the fraction field of a henselian local domain which is not a field. The proof uses a…
Translating between NIP integral domains and topological fields
Will Johnson
We prove that definable ring topologies on NIP fields are closely connected to NIP integral domains. More precisely, we show that up to elementary equivalence, any NIP topological…
A note on one-variable theorems for NSOP
Will Johnson
We give an example of an SOP theory , such that any -formula with is NSOP. We show that any such must have the independence property. We also give a s…
The classification of dp-minimal integral domains
Christian d'Elbée, Yatir Halevi, Will Johnson
We classify dp-minimal integral domains, building off the existing classification of dp-minimal fields and dp-minimal valuation rings. We show that if R is a dp-minimal integral do…
Generic differentiability and -minimal groups
Will Johnson
We prove generic differentiability in -minimal theories, strengthening an earlier result of Kuijpers and Leenknegt. Using this, we prove Onshuus and Pillay's -minimal analogu…
Visceral theories without assumptions
Will Johnson
Let be a theory with a definable topology. is t-minimal in the sense of Mathews if every definable set in one variable has finite boundary. If is t-minimal, we show tha…
C-minimal fields have the exchange property
Will Johnson
We show that C-minimal fields (i.e., C-minimal expansions of ACVF) have the exchange property, answering a question of Haskell and Macpherson. Additionally, we strengthen some theo…
A note on geometric theories of fields
Will Johnson, Jinhe Ye
Let be a complete theory of fields, possibly with extra structure. Suppose that model-theoretic algebraic closure agrees with field-theoretic algebraic closure, or more general…