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Kategorielle Mengenlehre: Eine Charakterisierung der Kategorie der Klassen und Abbildungen. (German) Zbl 0292.02050


MSC:

03E30 Axiomatics of classical set theory and its fragments
18A15 Foundations, relations to logic and deductive systems
18B05 Categories of sets, characterizations

References:

[1] Bernays, P.: A system of axiomatic set theory I?VII. J. Symb. Logic2, 65-77 (1937),6, 1-7 (1941),7, 65-89 (1942),7, 133-145 (1942),8, 89-106 (1943),13, 65-79 (1948),19, 81-96 (1954) · Zbl 0019.29403 · doi:10.2307/2268862
[2] Cole, J. C.: Categories of sets and models of set theory. Ph.D.-Thesis, University of Sussex (England), Brighton 1972
[3] Gödel, K.: The consistency of the axioms of choice and of the generalized continuumhypothesis with the axioms of set theory. Princeton: Princeton University Press 1940
[4] Gray, J. W.: The meeting of the Midwest Category Seminar in Zürich. In: Reports of the Midwest Category Seminar V. Berlin-Heidelberg-New York: Springer 1971 · Zbl 0222.18001
[5] Lawvere, F. W.: An elementary theory of the category of sets. Proc. Nat. Acad. Sciences52, 1506-1511 (1964) · Zbl 0141.00603 · doi:10.1073/pnas.52.6.1506
[6] Lawvere, F. W.: The category of categories as a foundation for mathematics. In: Proceedings on the conference on categorical algebra (La Jolla 1965). Berlin-Heidelberg-New York: Springer 1966 · Zbl 0158.26401
[7] Lawvere, F. W., Tierney, M.: Elementary topos. Lectures at the Midwest-Category Seminar in Zürich, August 1970. Zusammengefaßt in [4]
[8] Mitchell, W.: Boolean topoi and the theory of sets. J. Pure Appl. Algebra2, 261-274 (1972) · Zbl 0245.18001 · doi:10.1016/0022-4049(72)90006-0
[9] Osius, G.: Categorical set theory: A characterization of the category of sets. J. Pure Appl. Algebra4, 79-119 (1974) · Zbl 0282.02027 · doi:10.1016/0022-4049(74)90032-2
[10] Pumplün, D.: Kategorien I, Vorlesungsausarbeitung. Math. Inst. Universität Münster, 1972
[11] Rubin, J.: Set theory for the mathematician. San Francisco-Cambridge-London-Amsterdam: Holden Day 1967 · Zbl 0183.01301
[12] Schubert, H.: Kategorien I, II. Berlin-Heidelberg-New York: Springer 1970
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