Computable Folner sequences of amenable groups

2025/09/15 by Karol Duda, Duda, Karol, Aleksander Ivanov +1
Computer Science · #Computability, Logic, AI Algorithms #FOS: Mathematics #Group Theory (math.GR) #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2509.11806

openalex publication_date 2025/09/15 · openalex created_date 2025/10/12 · openalex updated_date 2026/07/28

Abstract

The paper considers computable Folner sequences in computably enumerable amenable groups. We extend some basic results of M. Cavaleri on existence of such sequences to the case of groups where finite generation is not assumed. We also initiate some new directions in this topic, for example complexity of families of effective Folner sequences. Possible extensions of this approach to metric groups are also discussed. This paper also contains some unpublished results from the paper of the first author arXiv:1904.02640.

Citations

• Computable paradoxical decompositions
• Generic algebraic properties in spaces of enumerated groups
• On first order amenability
• Degrees of and lowness for isometric isomorphism
• Amenability, connected components, and definable actions
• On effective Birkhoff's ergodic theorem for computable actions of\n amenable groups
• Structurable equivalence relations
• Amenability and ergodic properties of topological groups: from Bogolyubov onwards
• Medvedev degrees of two-dimensional subshifts of finite type
• Sofic representations of amenable groups
• Groups, measures, and the NIP

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