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APAL
2010

Cardinal sequences of LCS spaces under GCH

13 years 11 months ago
Cardinal sequences of LCS spaces under GCH
Let C() denote the class of all cardinal sequences of length associated with compact scattered spaces. Also put C() = {f C() : f(0) = = min[f() : < ]}. If is a cardinal and < ++ is an ordinal, we define D() as follows: if = , D() = {f {, 1} : f(0) = }, and if is uncountable, D() = {f {, + } : f(0) = , f-1 {} is < -closed and successor-closed in }. We show that for each uncountable regular cardinal and ordinal < ++ it is consistent with GCH that C() is as large as possible, i.e. C() = D(). This yields that under GCH for any sequence f of regular cardinals of length the following statements are equivalent: (1) f C() in some cardinal preserving and GCH-preserving generic-extension of the ground model. (2) for some natural number n there are infinite regular cardinals 0 > 1 >
Juan Carlos Martinez, Lajos Soukup
Added 08 Dec 2010
Updated 08 Dec 2010
Type Journal
Year 2010
Where APAL
Authors Juan Carlos Martinez, Lajos Soukup
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