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

Andrzej Szymański

Commentationes Mathematicae Universitatis Carolinae (2011)

  • Volume: 52, Issue: 3, page 463-471
  • ISSN: 0010-2628

Abstract

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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 ℕ * . Prikry’s poset is used to settle a problem by Fedeli regarding possible values of very weak caliber.

How to cite

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Szymański, Andrzej. "On $\pi $-caliber and an application of Prikry’s partial order." Commentationes Mathematicae Universitatis Carolinae 52.3 (2011): 463-471. <http://eudml.org/doc/247029>.

@article{Szymański2011,
abstract = {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.},
author = {Szymański, Andrzej},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {nowhere dense; point-$\kappa $ family; $\pi $-caliber; nowhere dense; point- family; -caliber},
language = {eng},
number = {3},
pages = {463-471},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On $\pi $-caliber and an application of Prikry’s partial order},
url = {http://eudml.org/doc/247029},
volume = {52},
year = {2011},
}

TY - JOUR
AU - Szymański, Andrzej
TI - On $\pi $-caliber and an application of Prikry’s partial order
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2011
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 52
IS - 3
SP - 463
EP - 471
AB - 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.
LA - eng
KW - nowhere dense; point-$\kappa $ family; $\pi $-caliber; nowhere dense; point- family; -caliber
UR - http://eudml.org/doc/247029
ER -

References

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  11. Prikry K., Changing measurable cardinals into accessible cardinals, Dissertationes Math. 68 (1970). MR0262075
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