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arXiv · 2609.05711

A counterexample to Petrykowski's conjecture

Artem Chernikov
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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, Krupi\'nski, Moconja, Pillay, and Ramsey, and gives a counterexample to Petrykowski's conjecture.

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Artem Chernikov. 2026-09-04. A counterexample to Petrykowski's conjecture. https://arxiv.org/abs/2609.05711

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