• Publications
  • Influence
Tame Topology and O-Minimal Structures
TLDR
I first want to thank Professor Brown for his kind introduction. Expand
  • 668
  • 52
DEFINABLE SETS IN ORDERED STRUCTURES. I
This paper introduces and begins the study of a well-behaved class of linearly ordered structures, the ¢minimal structures. The definition of this class and the corresponding class of theories, theExpand
  • 293
  • 11
Weakly o-minimal structures and real closed fields
A linearly ordered structure is weakly o-minimal if all of its definable sets in one variable are the union of finitely many convex sets in the structure. Weakly o-minimal structures were introducedExpand
  • 134
  • 11
  • PDF
ONE-DIMENSIONAL ASYMPTOTIC CLASSES OF FINITE STRUCTURES
A collection C of finite L-structures is a 1-dimensional asymptotic class if for every m ∈ N and every formula φ(x, y), where y = (y 1 ,...,y m ): (i) There is a positive constant C and a finite setExpand
  • 46
  • 11
  • PDF
Definable Compactness and Definable Subgroups of o‐Minimal Groups
The paper introduces the notion of definable compactness and within the context of o-minimal structures proves several topological properties of definably compact spaces. In particular a definableExpand
  • 124
  • 8
Definable Types in O-Minimal Theories
TLDR
We show that every type over an M-minimal expansion -of R is definable is equivalent to N being a conservative extension of M, where DEFINITION. Expand
  • 67
  • 7
Definable sets in ordered structures
On introduit la notion de theorie O-minimale des structures ordonnees, une telle theorie etant telle que les sous-ensembles definissables de ses modeles soient particulierement simples
  • 208
  • 6
  • PDF
Structures having o-minimal open core
The open core of an expansion of a dense linear order is its reduct, in the sense of definability, generated by the collection of all of its open definable sets. In this paper, expansions of denseExpand
  • 70
  • 6
Expansions of o-minimal structures by dense independent sets
TLDR
We study the structure ( M , ( H ) H ∈ H ) of an o-minimal expansion of a densely ordered group and show that every open set definable in the structure is definably independent in M . Expand
  • 25
  • 6
  • PDF
On o-Minimal Expansions of Archimedean Ordered Groups
We study o-minimal expansions of Archimedean totally ordered groups. We first prove that any such expansion must be elementarily embeddable via a unique (provided some nonzero element is 0-definable)Expand
  • 29
  • 6
...
1
2
3
4
5
...