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Israel Journal of Mathematics

, Volume 6, Issue 4, pp 363–367 | Cite as

ω 1 can be measurable

Article

Abstract

It is shown that ifZF + the axiom of choice + “there is a measurable cardinal” is consistent thenZF + “ω 1 is measurable” is consistent. The corresponding model is a symmetric submodel of the Cohen-type extension which collapses the first measurable cardinal onto ω0.

Keywords

Boolean Algebra Cardinal Number Continuum Hypothesis Measurable Cardinal Converse Inclusion 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

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    P. J. Cohen,Set theory and the continuum hypothesis, New York, 1966.Google Scholar
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    A. Lévy and R. Solovay,Measurable cardinals and the continuum hypothesis, Israel J. of Math.,5 (1967), 234–248.MATHGoogle Scholar
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    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.Google Scholar
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    P. Vopěnka,General theory of ∇-models, Math. Univ. Carol.,8 (1967), 145–170.Google Scholar

Copyright information

© Hebrew University 1968

Authors and Affiliations

  • T. Jech
    • 1
    • 2
  1. 1.Department of MathematicsCharles UniversityPrague
  2. 2.Praha 8Czechoslovakia

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