Abstract
The Ordinal Register Machine (ORM) is one of several different machine models for infinitary computability. We classify, by complexity, the sets that can be decided quickly by ORMs. In particular, we show that the arithmetical sets are exactly those sets that can be decided by ORMs in times uniformly less than \({\ensuremath{\omega^\omega}}\). Further, we show that the hyperarithmetical sets are exactly those sets that can be decided by an ORM in time uniformly less than \(\omega_1^{CK}\).
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Hamkins, J.D., Linetsky, D., Miller, R. (2007). The Complexity of Quickly ORM-Decidable Sets. In: Cooper, S.B., Löwe, B., Sorbi, A. (eds) Computation and Logic in the Real World. CiE 2007. Lecture Notes in Computer Science, vol 4497. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73001-9_51
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DOI: https://doi.org/10.1007/978-3-540-73001-9_51
Publisher Name: Springer, Berlin, Heidelberg
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