Almost disjoint families and “never” cardinal invariants

Charles Morgan; Samuel Gomes da Silva

Commentationes Mathematicae Universitatis Carolinae (2009)

  • Volume: 50, Issue: 3, page 433-444
  • ISSN: 0010-2628

Abstract

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We define two cardinal invariants of the continuum which arise naturally from combinatorially and topologically appealing properties of almost disjoint families of sets of the natural numbers. These are the never soft and never countably paracompact numbers. We show that these cardinals must both be equal to ω 1 under the effective weak diamond principle ♦ ( ω , ω , < ) , answering questions of da Silva S.G., On the presence of countable paracompactness, normality and property ( a ) in spaces from almost disjoint families, Questions Answers Gen. Topology 25(2007), no. 1, 1–18, and give some information about the strength of this principle.

How to cite

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Morgan, Charles, and da Silva, Samuel Gomes. "Almost disjoint families and “never” cardinal invariants." Commentationes Mathematicae Universitatis Carolinae 50.3 (2009): 433-444. <http://eudml.org/doc/33326>.

@article{Morgan2009,
abstract = {We define two cardinal invariants of the continuum which arise naturally from combinatorially and topologically appealing properties of almost disjoint families of sets of the natural numbers. These are the never soft and never countably paracompact numbers. We show that these cardinals must both be equal to $\omega _1$ under the effective weak diamond principle $\diamondsuit (\omega ,\omega ,<)$, answering questions of da Silva S.G., On the presence of countable paracompactness, normality and property $(a)$ in spaces from almost disjoint families, Questions Answers Gen. Topology 25(2007), no. 1, 1–18, and give some information about the strength of this principle.},
author = {Morgan, Charles, da Silva, Samuel Gomes},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {almost disjoint families; parametrized weak diamond principles; property $(a)$; countable paracompactness; almost disjoint family; parametrized weak diamond principle; property (a); countable paracompactness},
language = {eng},
number = {3},
pages = {433-444},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Almost disjoint families and “never” cardinal invariants},
url = {http://eudml.org/doc/33326},
volume = {50},
year = {2009},
}

TY - JOUR
AU - Morgan, Charles
AU - da Silva, Samuel Gomes
TI - Almost disjoint families and “never” cardinal invariants
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2009
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 50
IS - 3
SP - 433
EP - 444
AB - We define two cardinal invariants of the continuum which arise naturally from combinatorially and topologically appealing properties of almost disjoint families of sets of the natural numbers. These are the never soft and never countably paracompact numbers. We show that these cardinals must both be equal to $\omega _1$ under the effective weak diamond principle $\diamondsuit (\omega ,\omega ,<)$, answering questions of da Silva S.G., On the presence of countable paracompactness, normality and property $(a)$ in spaces from almost disjoint families, Questions Answers Gen. Topology 25(2007), no. 1, 1–18, and give some information about the strength of this principle.
LA - eng
KW - almost disjoint families; parametrized weak diamond principles; property $(a)$; countable paracompactness; almost disjoint family; parametrized weak diamond principle; property (a); countable paracompactness
UR - http://eudml.org/doc/33326
ER -

References

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