We investigate the computability of countable subshifts in one dimension, and their members. Subshifts of Cantor-Bendixson rank two contain only eventually periodic elements. Any rank two subshift in 2 Z is decidable. Subshifts of rank three may contain members of arbitrary Turing degree. In contrast, effectively closed ( 0 1 ) subshifts of rank three contain only computable elements, but 0 1 subshifts of rank four may contain members of arbitrary 0 2 degree. There is no subshift of rank ω + 1.

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