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Publications Influence

Tame Topology and O-Minimal Structures

- C. Steinhorn
- Computer Science
- 2008

TLDR

668 52

DEFINABLE SETS IN ORDERED STRUCTURES. I

- A. Pillay, C. Steinhorn
- Mathematics
- 1 February 1986

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, the… Expand

293 11

Weakly o-minimal structures and real closed fields

- D. Macpherson, D. Marker, C. Steinhorn
- Mathematics
- 13 April 2000

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 introduced… Expand

134 11- PDF

ONE-DIMENSIONAL ASYMPTOTIC CLASSES OF FINITE STRUCTURES

- D. Macpherson, C. Steinhorn
- Mathematics
- 2008

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 set… Expand

46 11- PDF

Definable Compactness and Definable Subgroups of o‐Minimal Groups

- Y. Peterzil, C. Steinhorn
- Mathematics
- 1 June 1999

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 definable… Expand

124 8

Definable Types in O-Minimal Theories

- D. Marker, C. Steinhorn
- Mathematics, Computer Science
- J. Symb. Log.
- 1 March 1994

TLDR

67 7

Definable sets in ordered structures

- A. Pillay, C. Steinhorn
- Mathematics
- 1 July 1984

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

- Alfred Dolich, C. Miller, C. Steinhorn
- Mathematics
- 8 October 2009

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 dense… Expand

70 6

Expansions of o-minimal structures by dense independent sets

- Alfred Dolich, C. Miller, C. Steinhorn
- Mathematics, Computer Science
- Ann. Pure Appl. Log.
- 1 August 2016

TLDR

25 6- PDF

On o-Minimal Expansions of Archimedean Ordered Groups

- Michael C. Laskowski, C. Steinhorn
- Mathematics, Computer Science
- J. Symb. Log.
- 1 September 1995

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

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