Pi01 sets and tilings

Emmanuel Jeandel (1) , Pascal Vanier (1)

1 LIF - Laboratoire d'informatique Fondamentale de Marseille - UMR 6166

In this paper, we prove that given any Π1 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.

Mots clés: Tilings; Pi01 sets; computability; SFT

Domaines: Mathématique discrète [cs.DM]

Emmanuel Jeandel, Pascal Vanier. Pi01 sets and tilings. 2011. ⟨hal-00563458v1⟩