Combinatorial complexity in o-minimal geometry
نویسندگان
چکیده
منابع مشابه
Complexity in O - Minimal Geometry
In this paper we prove tight bounds on the combinatorial and topological complexity of sets defined in terms of n definable sets belonging to some fixed definable family of sets in an o-minimal structure. This generalizes the combinatorial parts of similar bounds known in the case of semi-algebraic and semi-Pfaffian sets, and as a result vastly increases the applicability of results on combinat...
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Preface These notes have served as a basis for a course in Pisa in Spring 1999. A parallel course on the construction of o-minimal structures was given by A. Macintyre. The content of these notes owes a great deal to the excellent book by L. van den Dries [vD]. Some interesting topics contained in this book are not included here, such as the Vapnik-Chervonenkis property. Part of the material wh...
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Definition 1.3. Let C be a monster model of a theory interpretable in o-minimal structure. • A set φ(x) is finite by o-minimal if there is some definable equivalence relation E with finite classes and domain φ(C and a definable binary relation < such that (φ(C)/E,<) together with the C-induced structure is an ominimal ordered set. • A type p(x) is finite by o-minimal if there is some finite by ...
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ژورنال
عنوان ژورنال: Proceedings of the London Mathematical Society
سال: 2009
ISSN: 0024-6115
DOI: 10.1112/plms/pdp031