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Set theory over classes

Seria
Rozprawy Matematyczne tom/nr w serii: 106 wydano: 1973
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Warianty tytułu
Abstrakty
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CONTENTS
1. Introduction................................................................................................................ 5
2. General view on sets and classes....................................................................... 6
3. The elementary theory of classes, relations, and functions............................ 10
4. The general set theory over classes.................................................................... 18
5. The M-comprehension schema............................................................................ 25
6. Further considerations on ZF+M-Comp .............................................................. 30
7. A combination of set theory and stratification..................................................... 49
8. A generalization of stratification............................................................................. 67
9. Historical remark...................................................................................................... 59
References.................................................................................................................... 61
Słowa kluczowe
Tematy
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 106
Liczba stron
62
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CVI
Daty
wydano
1973
Twórcy
Bibliografia
  • [1] W. Ackermann, Zur Axiomatik der Mengenlehre, Math. Ann. 131 (1956), p. 336-345.
  • [2] P. Bernays and A.A. Fraenkel, Axiomatic set theory, Amsterdam 1958.
  • [3] N. Da Costa, On a set theory suggested by Dedecker and Ehresmann, I, II, Proc. Japan Acad. 45 (1969), p. 880-888.
  • [4] P. Dedecker, Introduction aux structures locales, Colloque de géometrie différentielle globale, Brussels 1958, p. 103-135.
  • [5] Ch. Ehresmann, Gattungen von lokalen Strukturen, Jahresbericht d. D. Math. Ver. 60 (1957), p. 49-77.
  • [6] E. Engeler and H. Röhrl, On the problem of foundations of category theory, Dialectica 23 (1969), p. 58-66.
  • [7] J. I. Friedman, Proper classes as members of extended sets, Math. Ann. 183 (1969), p. 232-240.
  • [8] K. Gödel, What is Cantor's Continuum Hypothesis, Amer. Math. Monthly 54 (1947), p. 515-525.
  • [9] J. Houdebine, Classes et ensembles, Séminaire Ch. Ehresmann, VI (1963).
  • [10] J. Houdebine, Théorie des classes et théorie des catégories, Thèse, Rennes, 1967.
  • [11] R. B. Jensen, On the consistency of a slight (?) modification of Quine's new foundations, in: Words and objections. Essays on the work of W. V. Quine. Edited by D. Davidson and J. Hintikka, Dordrecht 1969.
  • [12] M. Kühnrich, Zur Definition des geordneten Paares, Z. Math. Logik Grundlagen. Math. 13 (1967), p. 379-380.
  • [13] S. McLane, Locally small categories and the foundations of set theory. In: Infinitistic methods, Warszawa 1961. Proceedings of a 1959 conference, p. 25-43.
  • [14] A. Oberschelp, Eigentliche Klassen als Urelemente in der Mengenlehre, Math. Ann. 157 (1964), p. 234-260.
  • [15] A. Oberschelp, Sets and non-sets in set theory, Abstract, J. Symbolic Logic 29 (1964), p. 227.
  • [16] A. Oberschelp, Axiomatische Mengenlehre, Mimeographed lecture- notes, Hannover 1964.
  • [17] A. Oberschelp, Mengen, Relationen, Funktionen (ein einfaches für die Schule ausreichendes System der Mengenlehre), Math. Phys. Semesterber. 14 (1967), p. 1-40.
  • [18] A. Oberschelp, A combination of set theory and stratification, Paper contributed to the IVth International Congress for Logic, Methodology, and Philosophy of Science, Bucharest 1971.
  • [19] G. Osius, Eine Erweiterung der NBG-Mengenlehre als Grundlage der Kategorientheorie, Mimeographed, Bielefeld 1970.
  • [20] W. V. Quine, New foundations for mathematical logic, Amer. Math. Monthly 44 (1937), p. 70-80, reprinted in [24].
  • [21] W. V. Quine, Mathematical logic, Cambridge, Mass. 1940, rev. ed. 1951.
  • [22] W. V. Quine, On ordered pairs, J. Symbolic Logic 10 (1945), p. 95-96.
  • [23] W. V. Quine, On what there is, Reviews of Metaphysics (1948), reprinted in [24].
  • [24] W. V. Quine, From a logical point of view, 9 Logico-Philosophical Essays, Cambridge, Mass. 1953.
  • [25] W. V. Quine, Set theory and its logic, Cambridge, Mass. 1963, rev. ed. 1969.
  • [26] J. B. Rosser, Logic for mathematicians, New York, Toronto, London 1953.
  • [27] J. E. Rubin, Set theory for the mathematician, San Francisco 1967.
  • [28] J. Schmidt, Mengenlehre I, Mannheim 1966.
  • [29] J. Sonner, On the formal definition of categories, Math. Z. 80. (1962), p. 163 -176.
  • [30] P. Suppes, Axiomatic set theory, Princeton 1960.
  • [31] H. Wang, On Zermelo's and von Neumann's axioms for set theory, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), p. 150-155.
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