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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Soft almost disjoint families


Author: Paul J. Szeptycki
Journal: Proc. Amer. Math. Soc. 130 (2002), 3713-3717
MSC (2000): Primary 03E17, 54A25, 54D20
Published electronically: May 14, 2002
MathSciNet review: 1920052
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Abstract: An almost disjoint family $A$ is said to be soft if there is an infinite set that meets each $a\in A$ in a nonempty but finite set. We consider the associated cardinal invariant defined to be the minimal cardinality of an almost disjoint family that is not soft. We show that this cardinal coincides with J. Brendle's cardinal $\mathfrak{ap}$.


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Additional Information

Paul J. Szeptycki
Affiliation: School of Analytic Studies and Information Technology, York University, Toronto, Ontario, Canada M3J 1P3
Email: szeptyck@yorku.ca

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06487-0
PII: S 0002-9939(02)06487-0
Keywords: Almost disjoint families, unbounded sets, weakly separated, property (a)
Received by editor(s): September 15, 2000
Received by editor(s) in revised form: July 25, 2001
Published electronically: May 14, 2002
Additional Notes: The author received partial support from NSERC grant 238944.
Communicated by: Alan Dow
Article copyright: © Copyright 2002 American Mathematical Society