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Displaying similar documents to “Around splitting and reaping”

Almost disjoint families and “never” cardinal invariants

Charles Morgan, Samuel Gomes da Silva (2009)

Commentationes Mathematicae Universitatis Carolinae

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We define two cardinal invariants of the continuum which arise naturally from combinatorially and topologically appealing properties of almost disjoint families of sets of the natural numbers. These are the never soft and never countably paracompact numbers. We show that these cardinals must both be equal to ω 1 under the effective weak diamond principle ( ω , ω , < ) , answering questions of da Silva S.G., On the presence of countable paracompactness, normality and property ( a ) in spaces from almost...