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Tame Topology and O-minimal Structures
  • L. Dries
  • Mathematics, Computer Science
  • 28 May 1998
TLDR
1. Some elementary results 2. Semialgebraic sets 3. Cell decomposition 4. Definable invariants: Dimension and Euler characteristic 5. The Vapnik-Chernovenkis property in o-minimal structures 6. Point-set topology. Expand
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Geometric categories and o-minimal structures
The theory of subanalytic sets is an excellent tool in various analytic-geometric contexts; see, for example, Bierstone and Milman [1]. Regrettably, certain “nice” sets—like { (x, x) : x > 0 } forExpand
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  • 42
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P-adic and real subanalytic sets
  • 301
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Dense pairs of o-minimal structures
The structure of definable sets and maps in dense elementary pairs of o-minimal expansions of ordered abelian groups is described. It turns out that a certain notion of “small definable set” plays aExpand
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T-Convexity and Tame Extensions
TLDR
I solve here some problems left open in “ T -convexity and Tame Extensions” [9]. Expand
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Remarks on Tarski's problem concerning (R, +, *, exp)
Publisher Summary The chapter presents the elementary theory of the structure (R , + , .), and the results could be extended to the structure (R, +, ., exp). Some aspects of on (R , + , .) areExpand
  • 109
  • 10
A generalization of the Tarski-Seidenberg theorem, and some nondefinability results
This article points out some remarkable facts implicit in the results of Lojasiewicz [LI] and Gabrielov [Ga]. An important consequence of Tarski's work [T] on the elementary theory of the reals is aExpand
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The Elementary Theory of Restricted Analytic Fields with Exponentiation
numbers with exponentiation is model complete. When we combine this with Hovanskii's finiteness theorem [9], it follows that the real exponential field is o-minimal. In o-minimal expansions of theExpand
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Dimension of Definable Sets, Algebraic Boundedness and Henselian Fields
  • L. Dries
  • Mathematics, Computer Science
  • Ann. Pure Appl. Log.
  • 12 December 1989
  • 93
  • 9
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