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An Algebraic Proof of Deuber's Theorem

Published online by Cambridge University Press:  01 June 1998

NEIL HINDMAN  and
DONA STRAUSS
NEIL HINDMAN
Affiliation:
Department of Mathematics, Howard University, Washington, DC 20059, USA (e-mail: nhindman@aol.com)
DONA STRAUSS
Affiliation:
Department of Pure Mathematics, Hull University, Hull, HU6 7RX, UK (e-mail: d.strauss@maths.hull.ac.uk)
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Abstract

Deuber's theorem states that, given any m, p, c, r in IN, there exist n, q, μ in IN such that, whenever an (n, q, cμ)-set is r-coloured, there is a monochrome (m, p, c)-set. This theorem has been used in conjunction with the algebraic structure of the Stone–Čech compactification βIN of IN to derive several strengthenings of itself. We present here an algebraic proof of the main results in βIN and derive Deuber's theorem as a consequence.

Type
Research Article
Information
Combinatorics, Probability and Computing , Volume 7 , Issue 2 , June 1998 , pp. 167 - 180
Copyright
1998 Cambridge University Press

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