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Soft almost disjoint families

Author(s): Paul J. Szeptycki
Journal: Proc. Amer. Math. Soc. 130 (2002), 3713-3717.
MSC (2000): Primary 03E17, 54A25, 54D20
Posted: May 14, 2002
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Abstract: An almost disjoint family 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 $\mathfrak{ap}$ .

References:

1.: J. Brendle Dow's principle and Q-sets, Canadian Mathematical Bulletin, 42 no.1 (1999) 13-24. MR 2000h:03093
2.: W. Just, P.J. Szeptycki and M.V. Matveev Some results on property (a), Topology and its Applications 100 (2000) 67-83. MR 2001j:54019
3.: P.J. Szeptycki and J.E. Vaughan, Almost disjoint families and property (a), Fundamenta Mathematicae 158 (1998) 229-240. MR 99j:54009
4.: S. Todorcevic, Partition Problems in Topology, Contemporary Mathematics v 84 American Mathematical Society (1989). MR 90d:04001

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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: 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
Posted: May 14, 2002
Additional Notes: The author received partial support from NSERC grant 238944.
Communicated by: Alan Dow
Copyright of article: Copyright 2002, American Mathematical Society


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