Turing degree spectra of minimal subshifts

Michael Hochman; Pascal Vanier

doi:10.1007/978-3-319-58747-9_15

Turing degree spectra of minimal subshifts

Michael Hochman ¹ Pascal Vanier ²

2 LACL - Laboratoire d'Algorithmique Complexité et Logique

Abstract : Subshifts are shift invariant closed subsets of $\Sigma^{\mathbb{Z}^d}$ , minimal subshifts are subshifts in which all points contain the same patterns. It has been proved by Jeandel and Vanier that the Turing degree spectra of non-periodic minimal subshifts always contain the cone of Turing degrees above any of its degree. It was however not known whether each minimal subshift's spectrum was formed of exactly one cone or not. We construct inductively a minimal subshift whose spectrum consists of an uncountable number of cones with disjoint base.

Keywords : Turing degree subshift minimal subshift spectra cone

Document type :

Conference papers

Domain :

Computer Science [cs] / Discrete Mathematics [cs.DM]

Mathematics [math] / Dynamical Systems [math.DS]

Computer Science [cs] / Logic in Computer Science [cs.LO]

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Turing degree spectra of minimal subshifts

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