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Idempotents in compact semigroups and Ramsey theory

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Abstract

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.

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Research supported by the National Science Foundation under Grant No. DMS86-05098.

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Furstenberg, H., Katznelson, Y. Idempotents in compact semigroups and Ramsey theory. Israel J. Math. 68, 257–270 (1989). https://doi.org/10.1007/BF02764984

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  • DOI: https://doi.org/10.1007/BF02764984

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