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A model-theoretic note on the Freiman–Ruzsa theorem

Selecta Mathematica volume 27, Article number: 53 (2021) Cite this article

Abstract

A non-quantitative version of the Freiman–Ruzsa theorem is obtained for finite stable sets with small tripling in arbitrary groups, as well as for (finite) weakly normal subsets in abelian groups.

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Acknowledgements

The authors wish to thank Gabriel Conant and Caroline Terry for many helpful conversations and useful comments on a previous version of this note.

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Authors and Affiliations

  1. Abteilung für Mathematische Logik, Mathematisches Institut, Albert-Ludwig-Universität Freiburg, Ernst-Zermelo-Straße 1, 79104, Freiburg, Germany

    Amador Martin-Pizarro & Daniel Palacín

  2. Department of Pure Mathematics and Mathematical Statistics, Centre for Mathematical Sciences, Wilberforce Road, Cambridge, CB3 0WB, UK

    Julia Wolf

Authors
  1. Amador Martin-Pizarro
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  2. Daniel Palacín
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  3. Julia Wolf
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Corresponding author

Correspondence to Daniel Palacín.

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The first two authors conducted research partially supported by MTM2017-86777-P as well as by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project Number 2100310201 and 2100310301, part of the ANR-DFG program GeoMod.

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Martin-Pizarro, A., Palacín, D. & Wolf, J. A model-theoretic note on the Freiman–Ruzsa theorem. Sel. Math. New Ser. 27, 53 (2021). https://doi.org/10.1007/s00029-021-00676-9

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  • DOI: https://doi.org/10.1007/s00029-021-00676-9

Keywords

  • Model theory
  • Local stability
  • Additive combinatorics
  • Freiman–Ruzsa

Mathematics Subject Classification

  • 03C13
  • 03C45
  • 11B30