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Measurable cardinals and the continuum hypothesis

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Abstract

Let ZFM be the set theory ZF together with an axiom which asserts the existence of a measurable cardinal. It is shown that if ZFM is consistent then ZFM is consistent with every sentence φ whose consistency is proved by Cohen’s forcing method with a set of conditions of cardinality <k. In particular, if ZFM is consistent then it is consistent with the continuum hypothesis and with its negation.

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Authors and Affiliations

  1. The Hebrew University of Jerusalem, Israel

    A. Lévy & R. M. Solovay

  2. University of California, Berkeley, California

    A. Lévy & R. M. Solovay

Authors
  1. A. Lévy
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  2. R. M. Solovay
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Additional information

The research of the first named author has been sponsored in part by the Information Systems Branch, Office of Naval Research, Washington, D.C. under Contract F-61052 67 C 0055; the second named author was partially supported by an NAS-NRC post-doctoral fellowship and by National Science Foundation grant GP-5632.

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Lévy, A., Solovay, R.M. Measurable cardinals and the continuum hypothesis. Israel J. Math. 5, 234–248 (1967). https://doi.org/10.1007/BF02771612

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  • DOI: https://doi.org/10.1007/BF02771612

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