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Measurable cardinals and the continuum hypothesis. (English) Zbl 0289.02044

MSC:
03E35 Consistency and independence results
03E55 Large cardinals
03E50 Continuum hypothesis and Martin’s axiom
03E30 Axiomatics of classical set theory and its fragments
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References:
[1] P. J. Cohen,Set theory and the continuum hypothesis, New York, 1966. · Zbl 0182.01301
[2] W. Easton,Powers of Regular Cardinals, doctoral dissertation, Princeton University, 1964.
[3] W. P. Hanf and D. Scott,Classifying inaccessible cardinals (abstract), Notices Amer. Math. Soc.,8 (1961), 445.
[4] R. Jensen,An imbedding theorem for countable ZF models (abstract), Ibid.,12 (1965), 720.
[5] H. J. Keisler and A. Tarski,From accessible to inaccessible cardinals, Fund. Math.,53 (1964), 225–308. · Zbl 0173.00802
[6] A. Lévy,Axiom schemata of strong infinity in axiomatic set theory, Pacific J. Math.,10 (1960), 223–238. · Zbl 0201.32602
[7] A. Lévy,Definability in Axiomatic Set Theory I, Logic, Methodology, and Philosophy of Science, Proceedings of the 1964 International Congress (Y. Bar-Hillel, ed.), Amsterdam, 1966, 127–151.
[8] K. McAloon,Some applications of Cohen’s method, doctoral dissertation, University of California, Berkeley, 1966.
[9] D. Scott,Measurable cardinals and constructible sets, Bull. Acad. Polon. Sci., Ser. des Sci. Math., Astr. et Phys.,9 (1961), 521–524. · Zbl 0154.00702
[10] D. Scott and R. Solovay,Boolean-valued people looking at set theory, To appear in the Proceedings of the 1967 Summer Institute on Set Theory in Los Angeles.
[11] J. H. Silver,The consistency of the generalized continuum hypothesis with the existence of a measurable cardinal (abstract), Notices Amer. Math. Soc.,13 (1966), 721.
[12] J. H. Silver,The independence of Kurepa’s conjecture and the unprovability of a two-cardinal conjecture in model theory (abstract), Ibid.,14 (1967), 415.
[13] R. Solovay,Independence results in the theory of cardinals. I, II. Preliminary Report (abstract), Ibid.,10 (1963), 595.
[14] R. Solovay,A model of set theory in which all sets of reals are Lebesgue measurable. To appear. · Zbl 0207.00905
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