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Semigroup Forum

, Volume 97, Issue 3, pp 471–477 | Cite as

Hindman’s theorem and idempotent types

  • Uri Andrews
  • Isaac GoldbringEmail author
Research Article
  • 52 Downloads

Abstract

Motivated by a question of Di Nasso, we show that Hindman’s theorem is equivalent to the existence of idempotent types in countable complete extensions of Peano Arithmetic.

Keywords

IP set Hindman’s theorem Idempotent type 

References

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    Di Nasso, M.: Hypernatural numbers as ultrafilters. In: Loeb, P.A., Wolff, M. (eds.) Nonstandard Analysis for the Working mathematician, 2nd edn. Springer, Berlin (2015)Google Scholar
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    Di Nasso, M., Tachtsis, E.: Idempotent ultrafilters without Zorn’s Lemma. Proc. Am. Math. Soc. 146, 397–411 (2018)MathSciNetCrossRefGoogle Scholar
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    Golan, G., Tsaban, B.: Hindman’s coloring theorem in arbitrary semigroups. J. Algebra 395, 111–120 (2013)MathSciNetCrossRefGoogle Scholar
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    Hindman, N.: The existence of certain ultra-filters on \({\mathbb{N}}\) and a conjecture of Graham and Rothschild. Proc. Am. Math. Soc. 36, 341–346 (1972)MathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of WisconsinMadisonUSA
  2. 2.Department of MathematicsUniversity of CaliforniaIrvineUSA

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