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Roland Hinnion [20]R. Hinnion [8]
  1. Positive Abstraction and Extensionality.Roland Hinnion & Thierry Libert - 2003 - Journal of Symbolic Logic 68 (3):828-836.
    It is proved in this paper that the positive abstraction scheme is consistent with extensionality only if one drops equality out of the language. The theory obtained is then compared with GPK, a wellknown set theory based on an extended positive comprehension scheme.
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  2.  34
    The Consistency Problem for Positive Comprehension Principles.M. Forti & R. Hinnion - 1989 - Journal of Symbolic Logic 54 (4):1401-1418.
  3.  18
    Naive Set Theory with Extensionality in Partial Logic and in Paradoxical Logic.Roland Hinnion - 1994 - Notre Dame Journal of Formal Logic 35 (1):15-40.
    Two distinct and apparently "dual" traditions of non-classical logic, three-valued logic and paraconsistent logic, are considered here and a unified presentation of "easy-to-handle" versions of these logics is given, in which full naive set theory, i.e. Frege's comprehension principle + extensionality, is not absurd.
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  4.  24
    Stratified and Positive Comprehension Seen as Superclass Rules Over Ordinary Set Theory.Roland Hinnion - 1990 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 36 (6):519-534.
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  5.  11
    Stratified and Positive Comprehension Seen as Superclass Rules Over Ordinary Set Theory.Roland Hinnion - 1990 - Mathematical Logic Quarterly 36 (6):519-534.
  6.  22
    Topological Models for Extensional Partial Set Theory.Roland Hinnion & Thierry Libert - 2008 - Notre Dame Journal of Formal Logic 49 (1):39-53.
    We state the consistency problem of extensional partial set theory and prove two complementary results toward a definitive solution. The proof of one of our results makes use of an extension of the topological construction that was originally applied in the paraconsistent case.
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  7.  24
    Extensionality in Zermelo-Fraenkel Set Theory.R. Hinnion - 1986 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 32 (1-5):51-60.
  8.  16
    Fixed-Points of Set-Continuous Operators.O. Esser, R. Hinnion & D. Dzierzgowski - 2000 - Mathematical Logic Quarterly 46 (2):183-194.
    In this paper, we study when a set-continuous operator has a fixed-point that is the intersection of a directed family. The framework of our study is the Kelley-Morse theory KMC– and the Gödel-Bernays theory GBC–, both theories including an Axiom of Choice and excluding the Axiom of Foundation. On the one hand, we prove a result concerning monotone operators in KMC– that cannot be proved in GBC–. On the other hand, we study conditions on directed superclasses in GBC– in order (...)
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  9.  9
    About the Coexistence of “Classical Sets” with “Non-Classical” Ones: A Survey.Roland Hinnion - 2003 - Logic and Logical Philosophy 11:79-90.
    This is a survey of some possible extensions of ZF to a larger universe, closer to the “naive set theory” (the universes discussed here concern, roughly speaking : stratified sets, partial sets, positive sets, paradoxical sets and double sets).
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  10.  3
    Extensionality in Zermelo‐Fraenkel Set Theory.R. Hinnion - 1986 - Mathematical Logic Quarterly 32 (1‐5):51-60.
  11.  3
    Ramifiable Directed Sets.Roland Hinnion - 1998 - Mathematical Logic Quarterly 44 (2):216-228.
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  12.  1
    Directed Sets and Malitz‐Cauchy‐Completions.Roland Hinnion - 1997 - Mathematical Logic Quarterly 43 (4):465-484.
    This is a study of the set of the Malitz-completions of a given infinite first-order structure, put in relation with properties of directed sets.
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  13.  22
    Tree‐Properties for Ordered Sets.Olivier Esser & Roland Hinnion - 2002 - Mathematical Logic Quarterly 48 (2):213-219.
    In this paper, we study the notion of arborescent ordered sets, a generalizationof the notion of tree-property for cardinals. This notion was already studied previously in the case of directed sets. Our main result gives a geometric condition for an order to be ℵ0-arborescent.
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  14.  11
    Tree-Properties for Ordered Sets.Olivier Esser & Roland Hinnion - 2002 - Mathematical Logic Quarterly 48 (2):213-219.
    In this paper, we study the notion of arborescent ordered sets, a generalizationof the notion of tree-property for cardinals. This notion was already studied previously in the case of directed sets. Our main result gives a geometric condition for an order to be ℵ0-arborescent.
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  15. A" Downwards Lowenheim-Skolem-Tarski Theorem" for Specific Uniform Structures.Roland Hinnion - 2013 - Logique Et Analyse 56 (222):149-156.
     
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  16.  4
    A General Cauchy-Completion Process for Arbitrary First-Order Structures.Roland Hinnion - 2007 - Logique Et Analyse 197:5-41.
  17.  4
    Combinatorial Criteria for Ramifiable Ordered Sets.R. Hinnion & O. Esser - 2001 - Mathematical Logic Quarterly 47 (4):539-556.
    The tree-property and its variants make sense also for directed sets and even for partially ordered sets. A combinatoria approach is developed here, with characterizations and criteria involving adequate families of special substructures of directed sets. These substructures form a natural hierarchy that is also investigated.
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  18.  6
    Correction to “Embedding Properties and Anti‐Foundation in Set Theory”.Roland Hinnion - 1989 - Mathematical Logic Quarterly 35 (6):574-574.
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  19.  17
    Correction to “Embedding Properties and Anti-Foundation in Set Theory”.Roland Hinnion - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (6):574-574.
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  20.  4
    Embedding Properties and Anti‐Foundation in Set Theory.Roland Hinnion - 1989 - Mathematical Logic Quarterly 35 (1):63-70.
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  21.  17
    Embedding Properties and Anti-Foundation in Set Theory.Roland Hinnion - 1989 - Zeitschrift fur mathematische Logik und Grundlagen der Mathematik 35 (1):63-70.
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  22.  11
    Large Cardinals and Ramifiability for Directed Sets.R. Hinnion & O. Esser - 2000 - Mathematical Logic Quarterly 46 (1):25-34.
    The notion of “ramifiability” , usually applied to cardinals, can be extended to directed sets and is put in relation here with familiar “large cardinal” properties.
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  23.  7
    Antifoundation and Transitive Closure in the System of Zermelo.Olivier Esser & Roland Hinnion - 1999 - Notre Dame Journal of Formal Logic 40 (2):197-205.
    The role of foundation with respect to transitive closure in the Zermelo system Z has been investigated by Boffa; our aim is to explore the role of antifoundation. We start by showing the consistency of "Z antifoundation transitive closure" relative to Z (by a technique well known for ZF). Further, we introduce a "weak replacement principle" (deductible from antifoundation and transitive closure) and study the relations among these three statements in Z via interpretations. Finally, we give some adaptations for ZF (...)
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  24.  12
    Book Review: Peter Aczel. Non-Well-Founded Sets. [REVIEW]R. Hinnion - 1989 - Notre Dame Journal of Formal Logic 30 (2):308-312.