Measurable cardinals and the continuum hypothesis

A. Lévy; R. M. Solovay

doi:10.1007/BF02771612

Measurable cardinals and the continuum hypothesis

A. Lévy^*
, R. M. Solovay

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

188 Scopus citations

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.

Original language	English
Pages (from-to)	234-248
Number of pages	15
Journal	Israel Journal of Mathematics
Volume	5
Issue number	4
DOIs	https://doi.org/10.1007/BF02771612
State	Published - Oct 1967

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Measurable cardinals and the continuum hypothesis

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