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On a combinatorial property of menas related to the partition property for measures on supercompact cardinals

Published online by Cambridge University Press:  12 March 2014

Kenneth Kunen  and
Donald H. Pelletier
Kenneth Kunen*
Affiliation:
University of Texas at Austin, Austin, Texas 77712
Donald H. Pelletier
Affiliation:
York University, Downsview, Ontario, CanadaM3J 1P3
*
University of Wisconsin, Madison, Wisconsin 53706
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Abstract

T.K. Menas [4, pp. 225–234] introduced a combinatorial property Χ(μ) of a measure μ on a supercompact cardinal κ and proved that measures with this property also have the partition property. We prove here that Menas' property is not equivalent to the partition property. We also show that if a is the least cardinal greater than κ such that Pκα bears a measure without the partition property, then α is inaccessible and -indescribable.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 2 , June 1983 , pp. 475 - 481
Copyright
Copyright © Association for Symbolic Logic 1983

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References

REFERENCES

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