11 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.  9
    Models for a Paraconsistent Set Theory.Thierry Libert - 2005 - Journal of Applied Logic 3 (1):15-41.
  3.  5
    Hypercubes of Duality.Thierry Libert - 2012 - In J.-Y. Beziau & Dale Jacquette (eds.), Around and Beyond the Square of Opposition. Birkhäuser. pp. 293--301.
  4.  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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  5.  16
    Alternative Set Theories.Thierry Libert, T. Forster, R. Holmes, Dov M. Gabbay, John Woods & Akihiro Kanamori - 2009 - In Dov Gabbay (ed.), The Handbook of the History of Logic. Elsevier.
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  6.  13
    Positive Frege and its Scott‐Style Semantics.Thierry Libert - 2008 - Mathematical Logic Quarterly 54 (4):410-434.
    We show that the untyped λ -calculus can be extended with Frege's interpretation of propositional notions, provided we restrict β -conversion to positive expressions. The system of illative λ -calculus so obtained admits a natural Scott-style semantics.
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  7.  12
    On Topological Set Theory.Thierry Libert & Olivier Esser - 2005 - Mathematical Logic Quarterly 51 (3):263-273.
    This paper is concerned with topological set theory, and particularly with Skala's and Manakos' systems for which we give a topological characterization of the models. This enables us to answer natural questions about those theories, reviewing previous results and proving new ones. One of these shows that Skala's set theory is in a sense compatible with any ‘normal’ set theory, and another appears on the semantic side as a ‘Cantor theorem’ for the category of Alexandroff spaces.
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  8.  20
    ZF and the Axiom of Choice in Some Paraconsistent Set Theories.Thierry Libert - 2003 - Logic and Logical Philosophy 11:91-114.
    In this paper, we present set theories based upon the paraconsistent logic Pac. We describe two different techniques to construct models of such set theories. The first of these is an adaptation of one used to construct classical models of positive comprehension. The properties of the models obtained in that way give rise to a natural paraconsistent set theory which is presented here. The status of the axiom of choice in that theory is also discussed. The second leads to show (...)
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  9.  62
    An Order-Theoretic Account of Some Set-Theoretic Paradoxes.Thomas Forster & Thierry Libert - 2011 - Notre Dame Journal of Formal Logic 52 (1):1-19.
    We present an order-theoretic analysis of set-theoretic paradoxes. This analysis will show that a large variety of purely set-theoretic paradoxes (including the various Russell paradoxes as well as all the familiar implementations of the paradoxes of Mirimanoff and Burali-Forti) are all instances of a single limitative phenomenon.
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  10.  5
    Positive Abstraction and Extensionality Revisited.Thierry Libert - 2008 - Logique Et Analyse 202:149-165.
  11.  26
    Semantics for Naive Set Theory in Many-Valued Logics.Thierry Libert - 2006 - In Johan van Benthem, Gerhard Heinzman, M. Rebushi & H. Visser (eds.), The Age of Alternative Logics. Springer. pp. 121--136.
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