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We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π 0 1 class P is a subshift if and only if there is a computable function F mapping 2 N to 2 N such that P is the set of itineraries of elements of 2 N. Π 0 1 subshifts are constructed in 2 N and in 2 Z which have no computable elements. We… (More)

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… (More)

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