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

 

On Kelley's intersection numbers


Authors: Fred Galvin and Karel Prikry
Journal: Proc. Amer. Math. Soc. 129 (2001), 315-323
MSC (2000): Primary 06E10, 28A60
Published electronically: July 27, 2000
MathSciNet review: 1707516
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Abstract:

We introduce a notion of weak intersection number of a collection of sets, modifying the notion of intersection number due to J.L. Kelley, and obtain an analogue of Kelley's characterization of Boolean algebras which support a finitely additive strictly positive measure. We also consider graph-theoretic reformulations of the notions of intersection number and weak intersection number.


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Additional Information

Fred Galvin
Affiliation: Department of Mathematics, University of Kansas, Lawrence, Kansas 66045
Email: galvin@math.ukans.edu

Karel Prikry
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455
Email: prikry@math.umn.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05561-1
PII: S 0002-9939(00)05561-1
Keywords: Boolean algebra, strictly positive measure, intersection number, weak intersection number, hypergraph, fractional chromatic number
Received by editor(s): July 7, 1998
Received by editor(s) in revised form: April 15, 1999
Published electronically: July 27, 2000
Additional Notes: The first author’s research was partially supported by NSF Grant DMS-9700796.
Communicated by: Alan Dow
Article copyright: © Copyright 2000 American Mathematical Society