  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.
