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Distributive and related ideals in generic extensions

Published online by Cambridge University Press:  22 January 2016

C. A. Johnson
C. A. Johnson*
Affiliation:
Mathematics Department, Keele University, Keele, Staffs. ST5 5BG, England
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Let κ: be a regular uncountable cardinal and I a κ-complete ideal on te. In [11] Kanai proved that the μ-distributivity of the quotient algebra P(κ)I is preserved under κ-C.C. μ-closed forcing. In this paper we extend Kanai’s result and also prove similar preservation results for other naturally occurring forms of distributivity. We also consider the preservation of two game theoretic properties of I and in particular, using a game theoretic equivalent of precipitousness we give a new proof of Kakuda’s theorem ([10]) that the precipitousness of I is preserved under κ-C.C. forcing.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 106 , June 1987 , pp. 91 - 100
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

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