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The Saturation of a Product of Ideals

Published online by Cambridge University Press:  20 November 2018

Stanley Wagon
Stanley Wagon*
Affiliation:
Smith College, Northampton, Massachussets
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In this note we discuss how the saturation I X J, where I, J are k-complete ideals on a regular uncountable cardinal K, depends on the saturation of I and J. We show that if 2k = k+ then the saturation of I X J is completely determined by the saturation of I and J . A consequence of a negative saturation result is that NSk X NSk is not k+-saturated, where NSk is the nonstationary ideal on k (even though it is still open whether NSk can be K+- saturated). We also discuss the preservation of precipitousness under certain products, obtaining a simple example of an ideal on k that is precipitous but not k+-saturated.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 32 , Issue 1 , 01 February 1980 , pp. 70 - 75
Copyright
Copyright © Canadian Mathematical Society 1980

References

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