多维SFT的图灵度
Turing degrees of multidimensional SFTs
摘要：
在本文中，我们感兴趣的可计算性方面的subshifts，特别是图灵度的2维SFTs（即平铺）。为了更精确，我们证明了任何\pizu子集$P$的$\{0,1\}^\NN$有一个SFT $X$，使$P\times\ZZ^2$是递归同胚$X\setminus U$其中$U$是一个可计算的点集。因此，如果$P$包含递归成员，则$P$和$X$具有完全相同的图灵度集合。另一方面，我们证明，如果$X$只包含非递归成员，它的一些成员总是有不同的，但可比的程度。这给出了一个相当完整的研究图灵度的SFT。
英文摘要：
In this paper we are interested in computability aspects of subshifts and in particular Turing degrees of 2-dimensional SFTs (i.e. tilings). To be more precise, we prove that given any \pizu subset $P$ of $\{0,1\}^\NN$ there is a SFT $X$ such that $P\times\ZZ^2$ is recursively homeomorphic to $X\setminus U$ where $U$ is a computable set of points. As a consequence, if $P$ contains a recursive member, $P$ and $X$ have the exact same set of Turing degrees. On the other hand, we prove that if $X$ contains only non-recursive members, some of its members always have different but comparable degrees. This gives a fairly complete study of Turing degrees of SFTs.
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