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A structural generalization of the Ramsey theorem

A structural generalization of the Ramsey theorem

A generalization of the Ramsey theorem is stated.This solves a problem of P. Erdös and others.The result has recent applications in the theory of ultrafilters and model theory.The Ramsey theorem [3] states: For all positive integers k,m,p there exists an n such that for every coloring c: [n] p -• …