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$$\Pi^{0}_{1}$$ sets and tilings. (English) Zbl 1333.03109
Ogihara, Mitsunori (ed.) et al., Theory and applications of models of computation. 8th annual conference, TAMC 2011, Tokyo, Japan, May 23–25, 2011. Proceedings. Berlin: Springer (ISBN 978-3-642-20876-8/pbk). Lecture Notes in Computer Science 6648, 230-239 (2011).
Summary: In this paper, we prove that given any $$\Pi^{0}_{1}$$ subset $$P$$ of $$\{0,1\}^{\mathbb N}$$ there is a tileset $$\tau$$ with a countable set of configurations $$C$$ such that $$P$$ is recursively homeomorphic to $$C \setminus U$$ where $$U$$ is a computable set of configurations. As a consequence, if $$P$$ is countable, this tileset has the exact same set of Turing degrees.
For the entire collection see [Zbl 1213.68052].

##### MSC:
 03D28 Other Turing degree structures 03D15 Complexity of computation (including implicit computational complexity) 52C20 Tilings in $$2$$ dimensions (aspects of discrete geometry)
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