This paper studies diophantine properties of sets definable in an o-minimal structure over the real field. The main theorem of the author's recent paper with A. J. Wilkie is refined, and used to deduce a strong result on the density of algebraic points of such sets. © 2009 Birkhäuser Verlag Basel/Switzerland
We survey the development of o-minimal structures from a geometric point of view and compare them wi...
There are three main parts to this thesis, all centred around ultraproducts of o-minimal structures....
Let $K\subseteq \mathbb{R}$ be a number field. Using techniques of discrete analysis, we prove that ...
This paper studies diophantine properties of sets definable in an o-minimal structure over the real ...
This thesis concerns the study of the density of rational and algebraic points in the transcendental...
Let $X\R^n$ be a set that is definable in an o-minimal structure over $R$. This article shows that i...
Let X ⊂ ℝn be a set that is definable in an o-minimal structure over M. This article shows that in a...
We prove some simple special cases, partly new, of results of André-Oort-Manin-Mumford type using an...
We prove that the semialgebraic, algebraic, and algebraic nonsingular points of a definable set in o...
O-minimality has had some striking applications to number theory. The utility of o-minimal structur...
AbstractWe present some recent results and problems concerning definable sets and functions in o-min...
Consider the vanishing locus of a real analytic function on $\mathbb{R}^n$ restricted to $[0,1]^n$. ...
We prove some instances of Wilkie's conjecture on the density of rational points on sets definable i...
We prove some instances of Wilkie’s conjecture on the density of rational points on sets definable i...
Abstract. In this paper we study the metric spaces that are definable in a polynomially bounded o-mi...
We survey the development of o-minimal structures from a geometric point of view and compare them wi...
There are three main parts to this thesis, all centred around ultraproducts of o-minimal structures....
Let $K\subseteq \mathbb{R}$ be a number field. Using techniques of discrete analysis, we prove that ...
This paper studies diophantine properties of sets definable in an o-minimal structure over the real ...
This thesis concerns the study of the density of rational and algebraic points in the transcendental...
Let $X\R^n$ be a set that is definable in an o-minimal structure over $R$. This article shows that i...
Let X ⊂ ℝn be a set that is definable in an o-minimal structure over M. This article shows that in a...
We prove some simple special cases, partly new, of results of André-Oort-Manin-Mumford type using an...
We prove that the semialgebraic, algebraic, and algebraic nonsingular points of a definable set in o...
O-minimality has had some striking applications to number theory. The utility of o-minimal structur...
AbstractWe present some recent results and problems concerning definable sets and functions in o-min...
Consider the vanishing locus of a real analytic function on $\mathbb{R}^n$ restricted to $[0,1]^n$. ...
We prove some instances of Wilkie's conjecture on the density of rational points on sets definable i...
We prove some instances of Wilkie’s conjecture on the density of rational points on sets definable i...
Abstract. In this paper we study the metric spaces that are definable in a polynomially bounded o-mi...
We survey the development of o-minimal structures from a geometric point of view and compare them wi...
There are three main parts to this thesis, all centred around ultraproducts of o-minimal structures....
Let $K\subseteq \mathbb{R}$ be a number field. Using techniques of discrete analysis, we prove that ...
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