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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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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

Karel Prikry
Affiliation: School of Mathematics, University of Minnesota, Minneapolis, Minnesota 55455

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