17 found
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  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.  20
    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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  3.  13
    Stratified and positive comprehension seen as superclass rules over ordinary set theory.Roland Hinnion - 1990 - Mathematical Logic Quarterly 36 (6):519-534.
  4.  26
    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.  12
    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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  6.  27
    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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  7.  16
    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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  8. A" downwards Lowenheim-Skolem-Tarski theorem" for specific uniform structures.Roland Hinnion - 2013 - Logique Et Analyse 56 (222):149-156.
     
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  9.  6
    A general Cauchy-completion process for arbitrary first-order structures.Roland Hinnion - 2007 - Logique Et Analyse 197:5-41.
  10.  9
    Correction to “Embedding Properties and Anti‐Foundation in Set Theory”.Roland Hinnion - 1989 - Mathematical Logic Quarterly 35 (6):574-574.
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  11.  18
    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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  12.  2
    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.  7
    Embedding Properties and Anti‐Foundation in Set Theory.Roland Hinnion - 1989 - Mathematical Logic Quarterly 35 (1):63-70.
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  14.  18
    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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  15.  5
    Ramifiable Directed Sets.Roland Hinnion - 1998 - Mathematical Logic Quarterly 44 (2):216-228.
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  16.  24
    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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  17.  16
    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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