Multiplicatively large sets and ergodic Ramsey theory
type: Item
instance of: scholarly article
title: Multiplicatively large sets and ergodic Ramsey theory
zbMATH Open document ID: 1093.11003
DOI: 10.1007/BF02775431
author: V. Bergelson
published in: Israel Journal of Mathematics
publication date: 2006-02-06T00:00:00Z
review text: By utilizing various ergodic multiple recurrence theorems (e.g., of \textit{H. Furstenberg} and \textit{Y. Katznelson} [``An ergodic Szemerédi theorem for IP-systems and combinatorial theory'', J. Anal. Math. 45, 117--168 (1985; Zbl 0605.28012)] and \textit{V. Bergelson} and \textit{R. McCutcheon} [``An ergodic IP polynomial Szemerédi theorem'', Mem. Am. Math. Soc. 695, 106 (2000; Zbl 0948.28010)] various reswulte on multiplicatively large sets are proven, demonstrating their rich combinatorical structure. Such sets also contain various configurations which one expects to find in additively large sets, in particuliar arbitrary long arithmetic progressions. The author very well achieved a high level of readability making this paper, dedicated to Furstenberg on the occasion of his retirement, accesible to as wide an audience as possible.
Mathematics Subject Classification ID: 11B05
Mathematics Subject Classification ID: 05D10
Mathematics Subject Classification ID: 37A45
zbMATH DE Number: 5003404
zbMATH Keywords: syndetic sets
zbMATH Keywords: amenable multiplicatively large sets
zbMATH Keywords: IP sets
reviewed by: Harald Rindler
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5003404