A density version of the Hales-Jewett theorem

@article{Furstenberg1991ADV,
  title={A density version of the Hales-Jewett theorem},
  author={Harry Furstenberg and Y. Katznelson},
  journal={Journal d’Analyse Math{\'e}matique},
  year={1991},
  volume={57},
  pages={64-119}
}
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References

SHOWING 1-10 OF 11 REFERENCES
An ergodic Szemerédi theorem for IP-systems and combinatorial theory
A density version of the Hales-Jewett theorem for k=3
An ergodic Szemerédi theorem for commuting transformations
The classical Poincar6 recurrence theorem asserts that under the action of a measure preserving transformation T of a finite measure space (X, ~, p.), every set A of positive measure recurs in the…
On sets of integers containing k elements in arithmetic progression
In 1926 van der Waerden [13] proved the following startling theorem : If the set of integers is arbitrarily partitioned into two classes then at least one class contains arbitrarily long arithmetic…
A Dual Form of Ramsey's Theorem
The ergodic theoretical proof of Szemerédi's theorem
Partial results were obtained previously by K. F. Roth (1952) who established the existence of arithmetic progressions of length three in subsets of Z of positive upper density, and by E. Szemeredi…
Idempotents in compact semigroups and Ramsey theory
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…
Some unifying principles in Ramsey theory
  • T. Carlson
  • Computer Science, Mathematics
    Discret. Math.
  • 1988
Ein Satz über Untermengen einer endlichen Menge
Regularity and Positional Games
1.Introduction. Suppose X is a set, 𝒞 a collection of sets (usually subsets of X), and N is cardinal number. Following the terminology of Rado [1], we say 𝒞 is N-regular in X if,for any partition…
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