Computability of countable subshifts

Authors:
Douglas Cenzer;Ali Dashti;Ferit Toska;Sebastian Wyman
Affiliations:
Department of Mathematics, University of Florida, Gainesville, Florida;Department of Mathematics, University of Florida, Gainesville, Florida;Department of Mathematics, University of Florida, Gainesville, Florida;Department of Mathematics, University of Florida, Gainesville, Florida
Venue:
CiE'10 Proceedings of the Programs, proofs, process and 6th international conference on Computability in Europe
Year:
2010

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Abstract

The computability of countable subshifts and their members is examined. Results include the following. Subshifts of Cantor-Bendixson rank one contain only eventually periodic elements. Any rank one subshift, in which every limit point is periodic, is decidable. Sub-shifts of rank two may contain members of arbitrary Turing degree. In contrast, effectively closed (Π10) subshifts of rank two contain only computable elements, but Π10 subshifts of rank three may contain members of arbitrary c. e. degree. There is no subshift of rank ω.