1 citations · 1 across the 6 of their papers we have counts for
8 papers
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.
Points on a curve with a power on a curve
Gareth Boxall
Let be irreducible closed algebraic curves, with . Suppose is not contained in an algebraic subgroup of $\mathbb{G}_m^N(…
On algebraic values of Weierstrass -functions
Gareth Boxall, Taboka Chalebgwa, Gareth Jones
Suppose that is a lattice in the complex plane and let be the corresponding Weierstrass -function. Assume that the point associated to in the standard fundamenta…
Rational values of transcendental functions and arithmetic dynamics
Gareth Boxall, Gareth Jones, Harry Schmidt
We count algebraic points of bounded height and degree on the graphs of certain functions analytic on the unit disk, obtaining a bound which is polynomial in the degree and in the…
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…