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Singular cardinals

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Abstract

The problem is studied of the existence of nonconstructive subsets of cardinals belonging to an original countable standard transitive model of ZF theory of sets that do not generate new subsets of smaller cardinals of this same model. It is found that a fairly extensive class of properties of the extended model is closely related to the corresponding properties of the original model.

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Literature cited

  1. P. S. Aleksandrov, Introduction to General Theory of Sets and Functions [in Russian], Moscow (1948).

  2. P. J. Cohen, Set Theory and the Continuum Hypothesis, Benjamin, New York (1966).

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  3. W. B. Easton, “Powers of regular cardinals,” Ann. Math. Logic,1 No. 2, 69–112 (1970).

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Authors and Affiliations

  1. M. V. Lomonosov Moscow State University, USSR

    V. Kanovei

Authors
  1. V. Kanovei
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Additional information

Translated from Matematicheskie Zametki, Vol. 13, No. 5, pp. 717–724, May, 1973.

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Kanovei, V. Singular cardinals. Mathematical Notes of the Academy of Sciences of the USSR 13, 429–433 (1973). https://doi.org/10.1007/BF01147473

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  • DOI: https://doi.org/10.1007/BF01147473

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