Distributive and related ideals in generic extensions
Keyword(s):
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.
1971 ◽
Vol 29
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pp. 304-305
1995 ◽
Vol 53
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pp. 978-979
1990 ◽
Vol 48
(4)
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pp. 460-461
2008 ◽
Vol 78
(1)
◽
pp. 3-8
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2007 ◽
Vol 23
(4)
◽
pp. 248-257
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Keyword(s):
Keyword(s):