O-minimal Structures and Real Analytic Geometry
نویسندگان
چکیده
منابع مشابه
Quasi-analytic Solutions of Analytic Ordinary Differential Equations and O-minimal Structures
It is well known that the non-spiraling leaves of real analytic foliations of codimension 1 all belong to the same o-minimal structure. Naturally, the question arises of whether the same statement is true for non-oscillating trajectories of real analytic vector fields. We show, under certain assumptions, that such a trajectory generates an o-minimal and model-complete structure together with th...
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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 by Dickmann, and they arise in several contexts. We here prove several fundamental results about weakly o-minimal structures. Foremost among these, we show that every weakly o-minimal ordered field ...
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In this paper we study (strongly) locally o-minimal structures. We first give a characterization of the strong local o-minimality. We also investigate locally o-minimal expansions of (R,+, <).
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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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ژورنال
عنوان ژورنال: Current Developments in Mathematics
سال: 1998
ISSN: 1089-6384,2164-4829
DOI: 10.4310/cdm.1998.v1998.n1.a4