Additive and Multiplicative Ramsey Theorems in ℕ – Some Elementary Results

DOI10.1017/S0963548300000638zbMath0794.05127OpenAlexW2011665643MaRDI QIDQ4289290

Neil Hindman, Vitaly Bergelson

Publication date: 24 May 1994

Published in: Combinatorics, Probability and Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1017/s0963548300000638

zbMATH Keywords

partitionsequencesaxiom of choiceStone-Čech compactificationRamsey theoremsRado theoremtheorem of Hindman

Mathematics Subject Classification ID

Ramsey theory (05D10) Arithmetic progressions (11B25) Semigroups (20M99)

Related Items (8)

Partitions and (\(m\) and \(n\)) sums of products ⋮ CONSERVATIVITY OF ULTRAFILTERS OVER SUBSYSTEMS OF SECOND ORDER ARITHMETIC ⋮ Topological properties of some algebraically defined subsets of \(\beta \mathbb{N}\) ⋮ On the interplay between additive and multiplicative largeness and its combinatorial applications ⋮ Additive and multiplicative Ramsey theory in the reals and the rationals ⋮ Force recurrence of semigroup actions ⋮ ON IDEMPOTENT ULTRAFILTERS IN HIGHER-ORDER REVERSE MATHEMATICS ⋮ Multiplicatively large sets and ergodic Ramsey theory

Cites Work

• Partitions and pairwise sums and products
• A density statement generalizing Schur's theorem
• The ideal structure of the space of \(\kappa\)-uniform ultrafilters on a discrete semigroup
• Topological dynamics and combinatorial number theory
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Studien zur Kombinatorik
• Finite sums from sequences within cells of a partition of N
• A short proof of Hindman's theorem
• Partitionen und lineare Gleichungssysteme
• Ultrafilters: Some old and some new results
• Partitions and Sums and Products of Integers
• Nonmetrizable Topological Dynamics and Ramsey Theory
• Unnamed Item

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