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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On Kelley’s intersection numbers
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by Fred Galvin and Karel Prikry PDF
Proc. Amer. Math. Soc. 129 (2001), 315-323 Request permission

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
  • 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
  • © Copyright 2000 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 129 (2001), 315-323
  • MSC (2000): Primary 06E10, 28A60
  • DOI: https://doi.org/10.1090/S0002-9939-00-05561-1
  • MathSciNet review: 1707516