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Intensional positive set theory

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Języki publikacji
EN
Abstrakty
EN
This paper shows that, via a simple kind of forcing, one can construct a pure term model for intensional positive set theory, where sets are defined by positive formulas and identifica- tions are ruled by equivalence of the defining formulas. Further one can also construct a model that "contains ZF".
Rocznik
Tom
Strony
107--125
Opis fizyczny
Bibliogr. 16 poz.
Twórcy
autor
  • Université Libre de Bruxelles C.P. 211 Boulevard du Triomphe 1050 Bruxelles, Belgium, rhinnion@ulb.ac.be
Bibliografia
  • [1] M. Boffa, Forcing et négation de l'axiome de fondement, Académie Royale de Belgique, Vol. 40 (1972).
  • [2] M. Boffa, The consistency of ZF +NF3, Mathematisches Forschunginstitut Oberwolfach, Tagungsbericht 9 (1987).
  • [3] O. Esser, An interpretation of the Zermelo-Fraenkel Set Theory and the Kelley-Morse Set Theory in a Positive Theory, Mathematical Logic Quarterly 43 (1999), pp. 369-377.
  • [4] O. Esser, On the consistency of a positive set theory, Mathematical Logic Quarterly 45 (1999), pp. 105-116.
  • [5] O. Esser, A model of a strong paraconsistent set theory, Notre Dame Journal of Formal Logic 44 (2003), to appear.
  • [6] M. Forti & R. Hinnion, The consistency problem for positive comprehension principles, The Journal of Symbolic Logic 54 (1989), pp. 1401-14198.
  • [7] M. Forti & F. Honsell, A general construction of hyperuniverses, Theoretical Computer Science 156 (1996), pp. 203-215.
  • [8] P.C. Gilmore, The consistency of partial set theory without extensionality, Proceedings of Symposia in Pure Mathematics 13 (1974), pp. 147-153.
  • [9] P.C. Gilmore, An intensional type theory : motivation and cut-elimination, The Journal of Symbolic Logic 66 (2001), pp. 283-400.
  • [10] P.C. Gilmore, Logicism Renewed : Logical Foundations for Mathematics and Computer Science, book to appear.
  • [11] R. Hinnion, Le paradoxe de Russell dans des versions positives de la théorie naïve des ensembles, Comptes Rendus de l'Académie des Sciences de Paris 304 (1987), pp. 307-310.
  • [12] R. Hinnion, Stratified and positive comprehension seen as superclass rules over ordinary set theory, Zeitschrift für mathematische Logik und Grundlagen der Mathematik 36 (1990), pp. 519-534.
  • [13] R. Hinnion, Naive set theory with extensionality in partial logic and in paradoxical logic, Notre Dame Journal of Formal Logic 35 (1994), pp. 15-40.
  • [14] R. Hinnion, About the coexistence of classical sets with non-classical ones : a survey, Logic and Logical Philosophy 11 (2003), pp. 79-90.
  • [15] R. Hinnion & T. Libert, Positive abstraction and extensionality, The Journal of Symbolic Logic 68 (2003), pp. 828-836.
  • [16] R.J. Malitz, Set theory in which the axiom of foundation fails, Ph.D. University of California (1976), unpublished (available from University Microfilms International, Ann. Arbor, Michigan 48106).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUJ3-0005-0010
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