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math.LO2026

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…

math.LO2026

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…

math.LO2026

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…

math.LO2025

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…

math.LO2025

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…

math.LO2025

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…