An approximate logic for measures

DOI10.1007/s11856-013-0054-3zbMath1298.03100arXiv1106.2854OpenAlexW2070321554MaRDI QIDQ2017144

Henry Towsner, Isaac Goldbring

Publication date: 25 June 2014

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1106.2854

zbMATH Keywords

first-order logicmodel theoryergodic theoryFurstenberg correspondenceapproximate measure logic

Mathematics Subject Classification ID

Extremal problems in graph theory (05C35) Hypergraphs (05C65) Enumeration in graph theory (05C30) General groups of measure-preserving transformations (28D15) Generalized Ramsey theory (05C55) Ramsey theory (05D10) Applications of model theory (03C98)

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Cites Work

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• Deducing the multidimensional Szemerédi theorem from an infinitary removal lemma
• Idempotents in compact semigroups and Ramsey theory
• A correspondence principle between (hyper)graph theory and probability theory, and the (hyper)graph removal Lemma
• Model theory.
• Ergodic behavior of diagonal measures and a theorem of Szemeredi on arithmetic progressions
• Generic structures and simple theories
• Simple theories
• Multiple recurrence and nilsequences (with an appendix by Imre Ruzsa)
• On asymptotic cones and quasi-isometry classes of fundamental groups of 3-manifolds
• Nonconventional ergodic averages and nilmanifolds
• The primes contain arbitrarily long arithmetic progressions
• The logic of integration
• Weak convergence of finite graphs, integrated density of states and a Cheeger type inequality
• Hypergraph regularity and the multidimensional Szemerédi theorem
• AN INVERSE THEOREM FOR THE GOWERSU⁴-NORM
• Stable group theory and approximate subgroups
• Convergence of diagonal ergodic averages
• Convergence of weighted polynomial multiple ergodic averages
• Szemerédi’s Regularity Lemma for Sparse Graphs
• Extremal problems on set systems
• Norm convergence of multiple ergodic averages for commuting transformations
• AN INVERSE THEOREM FOR THE GOWERS $U^3(G)$ NORM
• The counting lemma for regular k‐uniform hypergraphs
• A new proof of Szemerédi's theorem