5 citations · 10 across the 3 of their papers we have counts for
5 papers
One-dimensional definable topological spaces in o-minimal structures
Pablo Andújar Guerrero, Margaret E. M. Thomas
We study the properties of topological spaces , where is a definable set in an o-minimal structure and the topology on has a basis that is (uniformly) definable.…
An effective Pila-Wilkie theorem for sets definable using Pfaffian functions, with some diophantine applications
Gal Binyamini, Gareth O. Jones, Harry Schmidt +1
We prove an effective version of the Pila-Wilkie Theorem for sets definable using Pfaffian functions, providing effective estimates for the number of algebraic points of bounded he…
Directed sets and topological spaces definable in o-minimal structures
Pablo Andujar Guerrero, Margaret E. M. Thomas, Erik Walsberg
We study directed sets definable in o-minimal structures, showing that in expansions of ordered fields these admit cofinal definable curves, as well as a suitable analogue in expan…
Effective Pila--Wilkie bounds for unrestricted Pfaffian surfaces
Gareth O. Jones, Margaret E. M. Thomas
We prove effective Pila--Wilkie estimates for the number of rational points of bounded height lying on certain surfaces defined by Pfaffian functions. The class of surfaces to whic…
Ramsey growth in some NIP structures
Artem Chernikov, Sergei Starchenko, Margaret E. M. Thomas
We investigate bounds in Ramsey's theorem for relations definable in NIP structures. Applying model-theoretic methods to finitary combinatorics, we generalize a theorem of Bukh and…