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Ultrafilters and combinatorial number theory

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Number Theory Carbondale 1979

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 751))

Abstract

Our concern is with two areas of mathematics and a, possibly surprising, intimate connection between them. One is the branch of combinatorial number theory which deals with the ability, given a finite partition of ℕ, to find sums or products of certain descriptions lying in one cell of that partition. The other is the branch of set theoretic topology dealing with the existence of ultrafilters on ℕ which have specified properties. We shall present and, to the extent feasible, prove those major results in the former area with which we are familiar and many of the related results in the latter area.

This is an expanded version of an address presented to the Southern Illinois University Number Theory Conference, March 30 and 31, 1979.

The author gratefully acknowledges support received from the National Science Foundation via grant MCS 78-02330.

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Authors and Affiliations

  1. California State University, Los Angeles

    Neil Hindman

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  1. Neil Hindman
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Melvyn B. Nathanson

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© 1979 Springer-Verlag

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Hindman, N. (1979). Ultrafilters and combinatorial number theory. In: Nathanson, M.B. (eds) Number Theory Carbondale 1979. Lecture Notes in Mathematics, vol 751. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062706

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  • DOI: https://doi.org/10.1007/BFb0062706

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  • Print ISBN: 978-3-540-09559-0

  • Online ISBN: 978-3-540-34852-8

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