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Erdős semi-groups, arithmetic progressions, and Szemerédi’s theorem. (English) Zbl 1469.11016

Summary: In this paper, we introduce and study a certain type of sub-semigroup of \(\mathbb{R}/\mathbb{Z}\) which turns out to be closely related to Szemerédi’s theorem on arithmetic progressions.

MSC:

11B05 Density, gaps, topology
11B25 Arithmetic progressions
26A03 Foundations: limits and generalizations, elementary topology of the line
28A80 Fractals
37A44 Relations between ergodic theory and number theory
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