π10 Sets and tilings

Authors:
Emmanuel Jeandel;Pascal Vanier
Affiliations:
Laboratoire d'Informatique Fondamentale de Marseille;Laboratoire d'Informatique Fondamentale de Marseille
Venue:
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
Year:
2011

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Abstract

In this paper, we prove that given any Π10 subset P of {0, 1}N there is a tileset τ with a countable set of configurations C such that P is recursively homeomorphic to C \ 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.