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arXiv · 2609.04353

Medvedev degrees of SFTs on cocompact Fuchsian groups

Sebastián Barbieri·Nicanor Carrasco-Vargas·Paul Toussaint
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Abstract

We prove that for any cocompact Fuchsian group the class of Medvedev degrees attained by subshifts of finite type is the class of $\Pi_1^0$ degrees. This result relies on the construction of a rigid hierarchical structure in a graph model of the hyperbolic plane, and on the fact that every such group admits a representation in $\operatorname{PSL}_2(\mathbb{R})$ such that the matrices in the image have coefficients that are computable real numbers.

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Sebastián Barbieri, Nicanor Carrasco-Vargas, Paul Toussaint. 2026-09-03. Medvedev degrees of SFTs on cocompact Fuchsian groups. https://arxiv.org/abs/2609.04353

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