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PreprintarXiv licencearXiv

A counterexample to Petrykowski's conjecture

  • Artem Chernikov
Open at sourcePDFDOICite

Abstract

We construct a simple expansion of the theory of nonabelian free groups in which the group admits a global type with bounded left-translation orbit but is not definably amenable. This extends the construction of Chernikov, Hrushovski, Kruckman, Krupiński, Moconja, Pillay, and Ramsey, and gives a counterexample to Petrykowski's conjecture.

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Cite

BibTeXRIS
BibTeX
@misc{chernikov2026counterexample,
  title = {{A counterexample to Petrykowski's conjecture}},
  author = {Artem Chernikov},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.05711},
  eprint = {2609.05711},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.05711},
}
RIS
TY  - UNPB
TI  - A counterexample to Petrykowski's conjecture
AU  - Artem Chernikov
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.05711
UR  - https://arxiv.org/abs/2609.05711
AB  - We construct a simple expansion of the theory of nonabelian free groups in which the group admits a global type with bounded left-translation orbit but is not definably amenable. This extends the construction of Chernikov, Hrushovski, Kruckman, Krupiński, Moconja, Pillay, and Ramsey, and gives a counterexample to Petrykowski's conjecture.
ER  -