Idempotents in compact semigroups and Ramsey theory
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We prove a theorem about idempotents in compact semigroups. This theorem gives a new proof of van der Waerden’s theorem on arithmetic progressions as well as the Hales-Jewett theorem. It also gives an infinitary version of the Hales-Jewett theorem which includes results of T. J. Carlson and S. G. Simpson.
KeywordsLeft Ideal Minimal Ideal Free Semigroup Compact Semigroup Minimal Left Ideal
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