## 221 Citations

Poincaré recurrence and number theory: thirty years later

- Mathematics
- 2011

Hillel Furstenberg’s 1981 article in the Bulletin gives an elegant introduction to the interplay between dynamics and number theory, summarizing the major developments that occurred in the few years…

Multiple recurrence and the structure of probability-preserving systems

- Mathematics
- 2010

In 1975 Szemer\'edi proved the long-standing conjecture of Erd\H{o}s and Tur\'an that any subset of $\bbZ$ having positive upper Banach density contains arbitrarily long arithmetic progressions.…

An Introduction to WQO and BQO Theory (Preliminary Version)

- Mathematics
- 2004

First present totality proofs that rely on compactness. Then show that some of these results can be proved directly by induction on long wellorderings. Finally try to extract some converses. The…

Poincare's Legacies, Part II: pages from year two of a mathematical blog

- Mathematics
- 2009

index notation, 65 affine connection, 66 Bézout’s theorem, 3 baby Hurewicz theorem, 120 Bianchi identities, 71 Bishop-Gromov inequality, 165 Bishop-Gromov reduced volume, 165 Black-Scholes equation,…

2 PANDELIS DODOS The Hales – Jewett

- Mathematics
- 2017

We review and comment on a number of results in Ramsey theory obtained recently by the author in collaboration with V. Kanellopoulos, N. Karagiannis and K. Tyros. Among them are density versions of…

A structure theorem for stochastic processes indexed by the discrete hypercube

- MathematicsForum of Mathematics, Sigma
- 2021

Abstract Let A be a finite set with , let n be a positive integer, and let $A^n$ denote the discrete $n\text {-dimensional}$ hypercube (that is, $A^n$ is the Cartesian product of n many copies of A).…

Ramsey Theory for Layered Semigroups

- MathematicsElectron. J. Comb.
- 2021

By nonstandard and topological arguments, it is shown Ramsey statements on S are implied by the existence of "coherent" sequences in S, which allows for many results in Ramsey theory to be formalised and proved.

Appendix A : Measure Theory

- Mathematics
- 2014

Complete treatments of the results stated in this appendix may be found in any measure theory book; see for example Parthasarathy [281], Royden [321] or Kingman and Taylor [195]. A similar summary of…

## References

SHOWING 1-10 OF 11 REFERENCES

On sets of integers containing k elements in arithmetic progression

- Mathematics
- 1975

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…

The ergodic theoretical proof of Szemerédi's theorem

- Mathematics
- 1982

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…

Regularity and Positional Games

- Economics
- 1963

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…

Some unifying principles in Ramsey theory

- Computer Science, MathematicsDiscret. Math.
- 1988

Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions

- Mathematics
- 1977

An ergodic Szemerédi theorem for commuting transformations

- Mathematics
- 1978

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…