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An Algebraic Proof of Deuber's Theorem

Published online by Cambridge University Press:  01 June 1998

Department of Mathematics, Howard University, Washington, DC 20059, USA (e-mail:
Department of Pure Mathematics, Hull University, Hull, HU6 7RX, UK (e-mail:


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.

Research Article
1998 Cambridge University Press

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