Add to ORKGThis thesis concerns the study of the density of rational and algebraic points in the transcendental part of sets that are definable in o-minimal structures. An o-minimal version of a reparametrisation result of Yosef Yomdin is proved, Yomdin's result being the prototype of a result used to prove the Pila-Wilkie theorem. Subsequently we concentrate on a specific o-minimal structure, the real exponential field, and prove some partial results towards a conjecture of Wilkie concerning the particular paucity of rational points in sets definable in this structure. 2.EThOS - Electronic Theses Online ServiceGBUnited Kingdo
O-minimality has had some striking applications to number theory. The utility of o-minimal structur...
Let $K\subseteq \mathbb{R}$ be a number field. Using techniques of discrete analysis, we prove that ...
This work stems from an ongoing investigation into the distribution of ra-tional points lying on par...
This paper studies diophantine properties of sets definable in an o-minimal structure over the real ...
This paper studies diophantine properties of sets definable in an o-minimal structure over the real ...
We prove some simple special cases, partly new, of results of André-Oort-Manin-Mumford type using an...
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...
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 use a result due to Rolin, Speissegger, and Wilkie to show that definable sets in certain o-minim...
There are three main parts to this thesis, all centred around ultraproducts of o-minimal structures....
We use a result due to Rolin, Speissegger, and Wilkie to show that definable sets in certain o-minim...
Thesis (MSc)--Stellenbosch University, 2021.ENGLISH ABSTRACT: We investigate the behaviour of algebr...
Consider the vanishing locus of a real analytic function on $\mathbb{R}^n$ restricted to $[0,1]^n$. ...
O-minimality has had some striking applications to number theory. The utility of o-minimal structur...
Let $K\subseteq \mathbb{R}$ be a number field. Using techniques of discrete analysis, we prove that ...
This work stems from an ongoing investigation into the distribution of ra-tional points lying on par...
This paper studies diophantine properties of sets definable in an o-minimal structure over the real ...
This paper studies diophantine properties of sets definable in an o-minimal structure over the real ...
We prove some simple special cases, partly new, of results of André-Oort-Manin-Mumford type using an...
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...
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 use a result due to Rolin, Speissegger, and Wilkie to show that definable sets in certain o-minim...
There are three main parts to this thesis, all centred around ultraproducts of o-minimal structures....
We use a result due to Rolin, Speissegger, and Wilkie to show that definable sets in certain o-minim...
Thesis (MSc)--Stellenbosch University, 2021.ENGLISH ABSTRACT: We investigate the behaviour of algebr...
Consider the vanishing locus of a real analytic function on $\mathbb{R}^n$ restricted to $[0,1]^n$. ...
O-minimality has had some striking applications to number theory. The utility of o-minimal structur...
Let $K\subseteq \mathbb{R}$ be a number field. Using techniques of discrete analysis, we prove that ...
This work stems from an ongoing investigation into the distribution of ra-tional points lying on par...