AI 中文总结
该研究证明余紧富克斯群上有限型子转移的梅德韦杰夫度类为Π₁⁰度类，通过构造双曲平面图模型的刚性分层结构及利用可计算实数表示完成证明。
AI 中文摘要
我们证明，对任意余紧富克斯群，有限型子转移所达到的梅德韦杰夫度类为Π₁⁰度类。该结果依赖于双曲平面图模型中刚性分层结构的构造，且依赖于这类群均存在PSL₂(ℝ)表示，使得像矩阵的系数为可计算实数。
英文摘要
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 admits a representation in $\operatorname{PSL}_2(\mathbb{R})$ such that the matrices in the image have coefficients that are computable real numbers.
Comments62 pages, but a staggering total of 51 figures
