Journal of Symbolic Logic

Finitude simple et structures o-minimalesFiniteness property implies o-minimality

Jean-Marie Lion

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Résumé

L’objet de ce texte est de montrer que des fonctions qui appartiennent à une famille vérifiant une propriété de finitude a priori non uniforme sont en fait définissables dans une structure o-minimale.

Abstract

We consider a family of differential algebras of real functions on real euclidean spaces, stable under right composition by affine maps. We prove that under a weak finiteness property, there is an o-minimal expansion of the ordered field of real numbers in which all these functions are definable.

Article information

Source
J. Symbolic Logic, Volume 67, Issue 4 (2002), 1616-1622.

Dates
First available in Project Euclid: 18 September 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1190150303

Digital Object Identifier
doi:10.2178/jsl/1190150303

Mathematical Reviews number (MathSciNet)
MR1955657

Zentralblatt MATH identifier
1042.03030

Subjects
Primary: 14P15: Real analytic and semianalytic sets [See also 32B20, 32C05]
Secondary: 03C64: Model theory of ordered structures; o-minimality 32B20: Semi-analytic sets and subanalytic sets [See also 14P15]

Citation

Lion, Jean-Marie. Finitude simple et structures o-minimales. J. Symbolic Logic 67 (2002), no. 4, 1616--1622. doi:10.2178/jsl/1190150303. https://projecteuclid.org/euclid.jsl/1190150303


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