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J. Duparc [3]Jacques Duparc [3]Jean Duparc [2]
  1.  31
    Wadge Hierarchy and Veblen Hierarchy Part I: Borel Sets of Finite Rank.J. Duparc - 2001 - Journal of Symbolic Logic 66 (1):56-86.
    We consider Borel sets of finite rank $A \subseteq\Lambda^\omega$ where cardinality of Λ is less than some uncountable regular cardinal K. We obtain a "normal form" of A, by finding a Borel set Ω, such that A and Ω continuously reduce to each other. In more technical terms: we define simple Borel operations which are homomorphic to ordinal sum, to multiplication by a countable ordinal, and to ordinal exponentiation of base K, under the map which sends every Borel set A (...)
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  2.  8
    The Wadge Order on the Scott Domain is Not a Well-Quasi-Order.Jacques Duparc & Louis Vuilleumier - 2020 - Journal of Symbolic Logic 85 (1):300-324.
    We prove that the Wadge order on the Borel subsets of the Scott domain is not a well-quasi-order, and that this feature even occurs among the sets of Borel rank at most 2. For this purpose, a specific class of countable 2-colored posets $\mathbb{P}_{emb} $ equipped with the order induced by homomorphisms is embedded into the Wadge order on the $\Delta _2^0 $-degrees of the Scott domain. We then show that $\mathbb{P}_{emb} $ admits both infinite strictly decreasing chains and infinite (...)
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  3.  8
    Some Remarks on Baire’s Grand Theorem.Riccardo Camerlo & Jacques Duparc - 2018 - Archive for Mathematical Logic 57 (3-4):195-201.
    We provide a game theoretical proof of the fact that if f is a function from a zero-dimensional Polish space to \ that has a point of continuity when restricted to any non-empty compact subset, then f is of Baire class 1. We use this property of the restrictions to compact sets to give a generalisation of Baire’s grand theorem for functions of any Baire class.
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  4.  4
    Williams Raymond, 1921-88.Alex Gallinicos & Jean Duparc - 1989 - Actuel Marx 5:7.
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  5.  5
    The Wadge Hierarchy of Petri Nets Ω-Languages.Jean-Pierre Ressayre, Olivier Finkel & Jacques Duparc - 2014 - In Dieter Spreen, Hannes Diener & Vasco Brattka (eds.), Logic, Computation, Hierarchies. De Gruyter. pp. 109-138.
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  6.  36
    The Steel Hierarchy of Ordinal Valued Borel Mappings.J. Duparc - 2003 - Journal of Symbolic Logic 68 (1):187-234.
    Given well ordered countable sets of the form $\lamphi$, we consider Borel mappings from $\lamphiom$ with countable image inside the ordinals. The ordinals and $\lamphiom$ are respectively equipped with the discrete topology and the product of the discrete topology on $\lamphi$. The Steel well-ordering on such mappings is defined by $\phi\minf\psi$ iff there exists a continuous function $f$ such that $\phi\leq\psi\circ f$ holds for any $x\in\lamphiom$. It induces a hierarchy of mappings which we give a complete description of. We provide, (...)
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