Hausdorff limits of Rolle leaves

Let be an o-minimal expansion of the real field. We introduce a class of Hausdorff limits, the T ∞ -limits over , that do not in general fall under the scope of Marker and Steinhorn’s definability-of-types theorem. We prove that if admits analytic cell decomposition, then every T ∞ -limit over is de...

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Veröffentlicht in:	Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2013-03, Vol.107 (1), p.79-89
Hauptverfasser:	Lion, Jean-Marie, Speissegger, Patrick
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Closures Differential Geometry Logic Mathematical and Computational Physics Mathematics Mathematics and Statistics Original Paper Theoretical
Online-Zugang:	Volltext
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Zusammenfassung:	Let be an o-minimal expansion of the real field. We introduce a class of Hausdorff limits, the T ∞ -limits over , that do not in general fall under the scope of Marker and Steinhorn’s definability-of-types theorem. We prove that if admits analytic cell decomposition, then every T ∞ -limit over is definable in the pfaffian closure of .
ISSN:	1578-7303 1579-1505
DOI:	10.1007/s13398-012-0089-z