Geodesic
On $\pi$-caliber and an application of Prikry's partial order
Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 3, pp. 463-471.

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We study the concept of $\pi$-caliber as an alternative to the well known concept of caliber. $\pi$-caliber and caliber values coincide for regular cardinals greater than or equal to the Souslin number of a space. Unlike caliber, $\pi$-caliber may take on values below the Souslin number of a space. Under Martin's axiom, $2^{\omega }$ is a $\pi$-caliber of $\mathbb{N}^{\ast}$. Prikry's poset is used to settle a problem by Fedeli regarding possible values of very weak caliber.
Classification : 03E35, 54A15, 54A38
Keywords: nowhere dense; point-$\kappa $ family; $\pi $-caliber 
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Szymanski, Andrzej. On $\pi$-caliber and an application of Prikry's partial order. Commentationes Mathematicae Universitatis Carolinae, Tome 52 (2011) no. 3, pp. 463-471. http://geodesic.mathdoc.fr/item/CMUC_2011__52_3_a11/