1,428 research outputs found

    On definably proper maps

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    In this paper we work in o-minimal structures with definable Skolem functions and show that a continuous definable map between Hausdorff locally definably compact definable spaces is definably proper if and only if it is proper morphism in the category of definable spaces. We give several other characterizations of definably proper including one involving the existence of limits of definable types. We also prove the basic properties of definably proper maps and the invariance of definably proper in elementary extensions and o-minimal expansions.Comment: 33 pages. arXiv admin note: text overlap with arXiv:1401.084

    Integration and Cell Decomposition in PP-minimal Structures

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    We show that the class of L\mathcal{L}-constructible functions is closed under integration for any PP-minimal expansion of a pp-adic field (K,L)(K,\mathcal{L}). This generalizes results previously known for semi-algebraic and sub-analytic structures. As part of the proof, we obtain a weak version of cell decomposition and function preparation for PP-minimal structures, a result which is independent of the existence of Skolem functions. %The result is obtained from weak versions of cell decomposition and function preparation which we prove for general PP-minimal structures. A direct corollary is that Denef's results on the rationality of Poincar\'e series hold in any PP-minimal expansion of a pp-adic field (K,L)(K,\mathcal{L}).Comment: 22 page

    Expansions of fields by angular functions

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