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Medvedev degrees of SFTs on cocompact Fuchsian groups
We prove that for any cocompact Fuchsian group the class of Medvedev degrees attained by subshifts of finite type is the class of $Π_1^0$ 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
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