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Some Consequences of Martin’s Axiom and the Negation of the Continuum Hypothesis

Published online by Cambridge University Press:  22 January 2016

Juichi Shinoda
Juichi Shinoda*
Affiliation:
Nagoya University
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W. Sierpisnki [3] demonstrated 82 propositions, called C1-C82, with the aid of the continuum hypothesis. D. A. Martin and R. M. Solovay remarked in [2] that 48 of these propositions followed from Martin’s axiom (MA), 23 were refuted by and three were independent of But the relation of the remaining eight propositions to has been unsettled.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 49 , March 1973 , pp. 117 - 125
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1973

References

[1] Kunen, K., Inaccessibility properties of cardinals, Doctoral Dissertation, Stanford University, 1968.Google Scholar
[2] Martin, D. A. and Solovay, R. M., Internal Cohen extensions, Annals of Math. Logic vol. 2 (1970) 143–178.Google Scholar
[3] Sierpinski, W., Hypothèse du contnu, Second Edition (Chelsea, New York, 1956).Google Scholar