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Displaying similar documents to “Cardinal functions on compact F-spaces and on weakly countably complete Boolean algebras”

σ-Entangled linear orders and narrowness of products of Boolean algebras

Saharon Shelah (1997)

Fundamenta Mathematicae

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We investigate σ-entangled linear orders and narrowness of Boolean algebras. We show existence of σ-entangled linear orders in many cardinals, and we build Boolean algebras with neither large chains nor large pies. We study the behavior of these notions in ultraproducts.

Constructions of thin-tall Boolean spaces.

Juan Carlos Martínez (2003)

Revista Matemática Complutense

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This is an expository paper about constructions of locally compact, Hausdorff, scattered spaces whose Cantor-Bendixson height has cardinality greater than their Cantor-Bendixson width.

On Monk’s questions

Saharon Shelah (1996)

Fundamenta Mathematicae

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We deal with Boolean algebras and their cardinal functions: π-weight π and π-character πχ. We investigate the spectrum of π-weights of subalgebras of a Boolean algebra B. Next we show that the π-character of an ultraproduct of Boolean algebras may be different from the ultraproduct of the π-characters of the factors.

Tightness and π-character in centered spaces

Murray Bell (1999)

Colloquium Mathematicae

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We continue an investigation into centered spaces, a generalization of dyadic spaces. The presence of large Cantor cubes in centered spaces is deduced from tightness considerations. It follows that for centered spaces X, πχ(X) = t(X), and if X has uncountable tightness, then t(X) = supκ : 2 κ ⊂ X. The relationships between 9 popular cardinal functions for the class of centered spaces are justified. An example is constructed which shows, unlike the dyadic and polyadic properties, that the...