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Abstrakty
A general forcing method is developed that allows to construct pure term models for (roughly speaking) predicative first-order partial set theory, where specific identification/differentiation rules hold. The applications bring new results about the links with intensionality and extensionality.
Słowa kluczowe
Czasopismo
Rocznik
Tom
Strony
47--69
Opis fizyczny
Bibliogr. 17 poz.
Twórcy
autor
- Universite Libre de Bruxelles, CP.211, Bd du Triomphe, B1050 Brussels, 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] O. Esser, On the consistency of a positive set theory, Mathematical Logic Quarterly 45 (1999), pp. 105-116.
- [3] O. Esser, A model of a strong paraconsistent set theory, Notre Dame Journal of Formal Logic 44 (2003).
- [4] 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.
- [5] O. Esser, Inconsistency of the axiom of choice with the positive theory GPK+1, Journal of Symbolic Logic 65 (2000), 1911-1916.
- [6] M. Forti & R. Hinnion, The consistency problem for positive comprehension principles, The Journal of Symbolic Logic 54 (1989), pp. 1401-1418.
- [7] P.C. Gilmore, The consistency of partial set theory without extensionality, Proceedings of Symposia in Pure Mathematics 13 (1974), pp. 147-153.
- [8] R. Hinnion, Le paradoxe de Russell dans des versions positives de la théorie naïvedes ensembles, Comptes Rendus de l'Académie des Sciences de Paris 304 (1987), pp. 307-310.
- [9] 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.
- [10] R. Hinnion, Intensional positive set theory, Reports on Mathematical Logic 40 (2006).
- [11] R. Hinnion, About the coexistence of classical sets with non-classical ones: a survey, Logic and Logical Philosophy 11 (2003), pp. 79-90.
- [12] M.R. Holmes, The axiom of antifoundation in Jensen's \New Foundations with Ur-Elements", Bulletin de la Société Mathématique de Belgique 43 (1991), série B, pp. 167-179.
- [13] M.R. Holmes, The set theoretical program of Quine succeeded (but nobody noticed) , Modern Logic 4 (1994), pp. 1-47.
- [14] M.R. Holmes, Elementary set theory with a universal set, Cahiers du Centre de Logique 10 (1998), Academia, Louvain-la-Neuve (Belgium), pp. 1-241.
- [15] M.R. Holmes, Subsystems of Quine's \New Foundations" with predicativity restrictions , Notre Dame Journal of Formal Logic 40, no2, pp. 183-196.
- [16] M.R. Holmes, Strong axioms of infinity in NFU, Journal of Symbolic Logic 66 (2001), no1, pp. 87-116.
- [17] A. Rigo, Uniformly continuous model theory, Ph.D. (2002), Université Libre de Bruxelles.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BUJ6-0021-0016