The Complexity of Quickly ORM-Decidable Sets

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 ωω . Further, we show that the hyperarithmetical sets are exactly those sets that can be decided by an ORM in time uniformly less than ωCK 1 . Key words: Ordinal, ordinal computation, infinite time computation, computability, register machine, arithmetical hierarchy, hyperarithmetical hierarchy, complexity

• Type: Conference
• Year: 2007
• Where: CIE
• Authors: Joel David Hamkins, David Linetsky, Russell G. Miller
• Keywords: Arithmetical Sets, CIE 2007, Ordinal Register Machine, Register Machine