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A model-theoretic note on the Freiman–Ruzsa theorem

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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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