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, 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 StoneˇCech 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.

• Type: Journal
• Year: 1998
• Where: CPC
• Authors: Neil Hindman, Dona Strauss
• Keywords: Algebraic Structure, CPC 1998, Monochrome, StoneˇCech Compactification βN