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On π -caliber and an application of Prikry’s partial order

Andrzej Szymański (2011)

Commentationes Mathematicae Universitatis Carolinae

We study the concept of π -caliber as an alternative to the well known concept of caliber. π -caliber and caliber values coincide for regular cardinals greater than or equal to the Souslin number of a space. Unlike caliber, π -caliber may take on values below the Souslin number of a space. Under Martin’s axiom, 2 ω is a π -caliber of * . Prikry’s poset is used to settle a problem by Fedeli regarding possible values of very weak caliber.

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