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Israel Journal of Mathematics

, Volume 68, Issue 3, pp 257–270 | Cite as

Idempotents in compact semigroups and Ramsey theory

  • H. Furstenberg
  • Y. Katznelson
Article

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.

Keywords

Left Ideal Minimal Ideal Free Semigroup Compact Semigroup Minimal Left Ideal 
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Copyright information

© The Weizmann Science Press of Israel 1989

Authors and Affiliations

  • H. Furstenberg
    • 1
  • Y. Katznelson
    • 2
  1. 1.The E. Landau Center for Research in Mathematical Analysis, Department of MathematicsThe Hebrew University of JerusalemJerusalemIsrael
  2. 2.Department of MathematicsStanford UniversityStanfordUSA

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