Abstract
Weak forms of the axiom of choice are defined, their set theoretical strength is investigated and as an application topological wellordering theorems are derived.
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Literatur
Aczel, J.: Realisation of topologies. Publ. Math. Debrecen3, 11–15 (1963).
Blass, A.: Ramsey's theorem. J. Symb. Logic42, 387–390 (1977).
Brunner, N.: Sequential compactness and AC. Notre Dame J. F. Logic. (Im Druck.)
Brunner, N.: Geordnete Läuchli Kontinuen. Fund. Math. (Im Druck.)
Cigler, J., Reichel, H. C.: Topologie. Mannheim: Bibliograph. Inst. 1978.
Comfort, W. W.: A Theorem of Stone Cech type without AC. Fund. Math.63, 97–100 (1968).
Engelking, R.: General Topology. Warszawa: PWN — Polish Sci. Publ. 1977.
Esenin-Volpin, A. S.: The unprovability of Souslin's hypothesis without AC. (Russian.) Dokl. Akad. Nauk SSSR96, 9–12 (1954).
Felgner, U.: Models of ZF. Lect. Notes Math. 223. Berlin-Heidelberg-New York: Springer. 1971.
Felgner, U., Jech, T. J.: Variants of AC. Fund. Math.79, 79–85 (1973).
Halpern, J. D.: A question of Tarski and a maximal theorem of Kurepa. Pac. J. Math.41, 111–121 (1972).
Hickman, J. L.: Groups in models of set theory. Bull. Austr. Math. Soc.14, 199–232 (1976).
Howard, P. E.: Limitations on FM. J. Symb. Logic38, 416–422 (1973).
Howard, P. E., Rubin, J. E.: AC and linear order. Fund. Math.97, 111–122 (1977).
Jech, T. J.: Eine Bemerkungzum AC. Časopis Pěst. Mat.93, 30–31 (1968).
Jech, T. J.: The Axion of Choice. Amsterdam-London: North Holland. 1973.
Juhasz, I.: Cardinal Functions in Topology. Amsterdam: Math. Centrum. 1980.
Kinna, W., Wagner, K.: Abschwächung des AC. Fund. Math.42, 75–82 (1955).
Kleinberg, E. M.: Ramsey's theorem. J. Symb. Logic34, 205–206 (1969).
Kurepa, G. D.: Cartesian multiplication and cellularity. Publ. Inst. Math. (Beograd)2, 121–139 (1962).
Läuchli, H.: AC in der Algebra. Comm. Math. Helv.37, 1–18 (1962).
Levy, A.: Definition of finiteness. Fund. Math.46, 1–13 (1958).
Levy, A.: Consequences of AC. Fund. Math.54, 135–157 (1964).
Lutzer, D. J.: Pixley Roy Topologies. Topol. Conf. Univ. Oklahoma 1978, pp. 139–158. Auburn, Alabama: Auburn Univ. 1979.
Pincus, D.: Independence proofs. Fund. Math.92, 113–130 (1976).
Simon, P.: Cardinal invariants. Comm. Math. Univ. Carolinae14, 205–213 (1973).
Soundararajan, T.: WeaklyT 2 spaces. Proc. Conf. Kanpur 1968, pp. 301–307. Prague: Academia. 1971.
Truss, J. K.:D-finite cardinals. Fund. Math.84, 187–208 (1974).
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Brunner, N. Dedekind-Endlichkeit und Wohlordenbarkeit. Monatshefte für Mathematik 94, 9–31 (1982). https://doi.org/10.1007/BF01369079
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DOI: https://doi.org/10.1007/BF01369079