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Local definable -theorem and a refinement
Gareth John Boxall, Charlotte Kestner, Tsinjo Rakotonarivo
We prove the definable -conjecture for NIP formulas in arbitrary first-order theories. We also prove a refinement and apply it to dense pairs.
Theories with distal Shelah expansions
Gareth Boxall, Charlotte Kestner
We show that a complete first-order theory is distal provided it has a model such that the theory of the Shelah expansion of is distal.
A special case of quasiminimality
Gareth Boxall
We deduce a special case of Zilber's quasiminimality conjecture, for the complex exponential field, from work of Henson and Rubel. Specifically, we deal with those subsets of $\mat…
The definable (p,q)-theorem for distal theories
Gareth Boxall, Charlotte Kestner
Answering a special case of a question of Chernikov and Simon, we show that any non-dividing formula over a model M in a distal NIP theory is a member of a consistent definable fam…
Expansions which introduce no new open sets
Gareth Boxall, Philipp Hieronymi
We consider the question of when an expansion of a topological structure has the property that every open set definable in the expansion is definable in the original structure. Thi…