Turing degree spectra of minimal subshifts

Michael Hochman 1 Pascal Vanier 2
1 Einstein Institute of Mathematics
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
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Communication dans un congrès
Computer Science - Theory and Applications - 12th International Computer Science Symposium in Russia, Jun 2017, Kazan, Russia. 2017, 〈10.1007/978-3-319-58747-9_15〉
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Dernière modification le : mercredi 20 juin 2018 - 10:36:01
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Michael Hochman, Pascal Vanier. Turing degree spectra of minimal subshifts. Computer Science - Theory and Applications - 12th International Computer Science Symposium in Russia, Jun 2017, Kazan, Russia. 2017, 〈10.1007/978-3-319-58747-9_15〉. 〈hal-01058198v4〉

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