Nonstandard methods in Ramsey theory and combinatorial number theory

DOI10.1007/978-3-030-17956-4zbMath1432.05001arXiv1709.04076OpenAlexW2756213202MaRDI QIDQ2415093

Martino Lupini, Mauro Di Nasso, Isaac Goldbring

Publication date: 20 May 2019

Published in: Lecture Notes in Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1709.04076

zbMATH Keywords

Ramsey theorynonstandard analysisultrafiltersstructural propertiesnon-commutative groupsproduct setvan der Waerden's theoremfinite embeddabilityBanach densitymonochromatic sumsapproximate groupJin's sumset theoremLeob measureremote realm

Mathematics Subject Classification ID

Research exposition (monographs, survey articles) pertaining to combinatorics (05-02) Other combinatorial number theory (11B75) Generalized Ramsey theory (05C55) Ramsey theory (05D10) Nonstandard models in mathematics (03H05) Non-Archimedean function theory (30G06) Nonstandard functional analysis (46S20) Nonstandard operator theory (47S20) Nonstandard measure theory (28E05) Introductory exposition (textbooks, tutorial papers, etc.) pertaining to mathematics in general (00-01) Nonstandard analysis (26E35) Research exposition (monographs, survey articles) pertaining to mathematics in general (00-02) Nonstandard topology (54J05)

Related Items (9)

Using Ultrafilters to Prove Ramsey-type Theorems ⋮ Ramsey theory for layered semigroups ⋮ RAMSEY’S COHEIRS ⋮ On Rado conditions for nonlinear Diophantine equations ⋮ Subsets of virtually nilpotent groups with the SBM property ⋮ Algebraic combinatorics in bounded induction ⋮ A short nonalgorithmic proof of the containers theorem for hypergraphs ⋮ On Supra-SIM Sets of Natural Numbers ⋮ The largest $(k,\ell )$-sum-free subsets

This page was built for publication: Nonstandard methods in Ramsey theory and combinatorial number theory