An Algebraic Proof of Deuber's Theorem

Deuber’s Theorem says that, given any m, p, c, r in N, there exist n, q, μ in N such that whenever an (n, q, c)-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 StoneČech compactification βN of N to derive several strengthenings of itself. We present here an algebraic proof of the main results in βN and derive Deuber’s Theorem as a consequence.