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. Subshifts of rank two may contain members of arbitrary Turing degree. In contrast, effectively closed (\(\Pi^0_1\)) subshifts of rank two contain only computable elements, but \(\Pi^0_1\) subshifts of rank three may contain members of arbitrary c. e. degree. There is no subshift of rank ω.
This research was partially supported by NSF grants DMS 0532644 and 0554841 and 652372.
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Cenzer, D., Dashti, A., Toska, F., Wyman, S. (2010). Computability of Countable Subshifts . In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_10
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