Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-17T16:58:45.325Z Has data issue: false hasContentIssue false

Finitude simple et structures o-minimales (Finiteness property implies o-minimality)

Published online by Cambridge University Press:  12 March 2014

Jean-Marie Lion*
Affiliation:
Irmar-Université De Rennes I Campus De Beaulieu 35042 Rennes Cedex, France, E-mail: [email protected]

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.

Type
Research Article
Copyright
Copyright © Association for Symbolic Logic 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

RéFéRENCES

[1]Gabrielov, A. M., Projections of semi-analytic sets, Functional Analysis audits Applications, vol. 2 (1968), pp. 282291.CrossRefGoogle Scholar
[2]Ilyashenko, Y. and Kaloshin, V., Bifurcation of planar and spatial polycycles : Arnold's program and its development, The Arnoldfest, Toronto 1997, Fields Institute Communication, 24, American Mathematical Society, pp. 241271, 1999.Google Scholar
[3]Karpinski, M. and Macintyre, A., A generalization of Wilkie's theorem of the complement, and an application to Pfaffian closure, Selecta Mathematica (New Series), vol. 5 (1999), no. 4, pp. 507516.CrossRefGoogle Scholar
[4]Khovanskii, A. G., Real analytic varieties with the finitness property and complex abelian integrals, Functional Analysis and its Applications, vol. 18 (1984), pp. 119127.CrossRefGoogle Scholar
[5]Lion, J.-M. and Rolin, J.-P., Volumes, Feuilles de Rolle de Feuilletages analytiques et Théorème de Wilkie, Annales de la Faculté des Sciences de Toulouse, vol. 7 (1998), no. 1, pp. 93112.Google Scholar
[6]Łojasiewicz, S., Ensembles semi-analytiques, 1965, preprint IHES.Google Scholar
[7]Moussu, R. and Roche, C. A., Théorie de Hovanskii et problème de Dulac, Inventiones Mathematicae, vol. 105 (1991), pp. 431441.CrossRefGoogle Scholar
[8]Speissegger, P., The pfaffian closure of an o-minimal structure, Journal für die Reine und Angewandte Mathematik, vol. 508 (1999), pp. 189211.CrossRefGoogle Scholar
[9]Tarski, A., A decision method for elementary algebra and geometry, University of California Press, Berkeley and Los Angeles, 1951, 2nd edition.CrossRefGoogle Scholar
[10]Thom, R., Un lemme sur les applications différentiahles, Boletin Sociedad Matemática Mexicana, vol. 2 (1965), no. 1, pp. 5971.Google Scholar
[11]van den Dries, L., Tame Topology and O-minimal Structures, Cambridge, 1998.CrossRefGoogle Scholar
[12]van den Dries, L. and Miller, C., Geometric categories and o-minimal structures, Duke Mathemaical Journal, vol. 84 (1996), no. 2, pp. 497540.Google Scholar
[13]Wilkie, A., A general theorem of the complement and some new o-minimal structures, Selecta Mathematica (New Series), vol. 5 (1999), pp. 189211.Google Scholar