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Keywords:
nowhere dense; point-$\kappa $ family; $\pi $-caliber
nowhere dense; point-$\kappa $ family; $\pi $-caliber
Summary:
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.
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