9 found
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  1.  16
    Topological Cell Decomposition and Dimension Theory in P-Minimal Fields.Pablo Cubides Kovacsics, Luck Darnière & Eva Leenknegt - 2017 - Journal of Symbolic Logic 82 (1):347-358.
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  2.  23
    Uniformly Defining Valuation Rings in Henselian Valued Fields with Finite or Pseudo-Finite Residue Fields.Raf Cluckers, Jamshid Derakhshan, Eva Leenknegt & Angus Macintyre - 2013 - Annals of Pure and Applied Logic 164 (12):1236-1246.
    We give a definition, in the ring language, of Zp inside Qp and of Fp[[t]] inside Fp), which works uniformly for all p and all finite field extensions of these fields, and in many other Henselian valued fields as well. The formula can be taken existential-universal in the ring language, and in fact existential in a modification of the language of Macintyre. Furthermore, we show the negative result that in the language of rings there does not exist a uniform definition (...)
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  3.  64
    A Version of P-Adic Minimality.Raf Cluckers & Eva Leenknegt - 2012 - Journal of Symbolic Logic 77 (2):621-630.
    We introduce a very weak language L M on p-adic fields K, which is just rich enough to have exactly the same definable subsets of the line K that one has using the ring language. (In our context, definable always means definable with parameters.) We prove that the only definable functions in the language L M are trivial functions. We also give a definitional expansion $L\begin{array}{*{20}{c}} ' \\ M \\ \end{array} $ of L M in which K has quantifier elimination, (...)
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  4.  7
    Clustered Cell Decomposition in P-Minimal Structures.Saskia Chambille, Pablo Cubides Kovacsics & Eva Leenknegt - 2017 - Annals of Pure and Applied Logic 168 (11):2050-2086.
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  5.  49
    Cell Decomposition and Definable Functions for Weak P‐Adic Structures.Eva Leenknegt - 2012 - Mathematical Logic Quarterly 58 (6):482-497.
    We develop a notion of cell decomposition suitable for studying weak p-adic structures definable). As an example, we consider a structure with restricted addition.
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  6.  14
    Reducts of P-Adically Closed Fields.Eva Leenknegt - 2014 - Archive for Mathematical Logic 53 (3-4):285-306.
    In this paper, we consider reducts of p-adically closed fields. We introduce a notion of shadows: sets Mf={∈K2∣|y|=|f|}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${M_f = \{ \in K^2 \mid |y| = |f|\}}$$\end{document}, where f is a semi-algebraic function. Adding symbols for such sets to a reduct of the ring language, we obtain expansions of the semi-affine language where multiplication is nowhere definable, thus giving a negative answer to a question posed by Marker, Peterzil and Pillay. The second (...)
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  7.  1
    Exponential-Constructible Functions in P-Minimal Structures.Saskia Chambille, Pablo Cubides Kovacsics & Eva Leenknegt - 2019 - Journal of Mathematical Logic 20 (2):2050005.
    Exponential-constructible functions are an extension of the class of constructible functions. This extension was formulated by Cluckers and Loeser in the context of semi-algebraic and sub-analytic structures, when they studied stability under integration. In this paper, we will present a natural refinement of their definition that allows for stability results to hold within the wider class of [Formula: see text]-minimal structures. One of the main technical improvements is that we remove the requirement of definable Skolem functions from the proofs. As (...)
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  8.  15
    Differentiation in P-Minimal Structures and a P-Adic Local Monotonicity Theorem.Tristan Kuijpers & Eva Leenknegt - 2014 - Journal of Symbolic Logic 79 (4):1133-1147.
  9.  89
    Cell Decomposition for Semibounded P-Adic Sets.Eva Leenknegt - 2013 - Archive for Mathematical Logic 52 (5-6):667-688.
    We study a reduct ${\mathcal{L}_*}$ of the ring language where multiplication is restricted to a neighbourhood of zero. The language is chosen such that for p-adically closed fields K, the ${\mathcal{L}_*}$ -definable subsets of K coincide with the semi-algebraic subsets of K. Hence structures (K, ${\mathcal{L}_*}$ ) can be seen as the p-adic counterpart of the o-minimal structure of semibounded sets. We show that in this language, p-adically closed fields admit cell decomposition, using cells similar to p-adic semi-algebraic cells. From (...)
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