We generalize ordinary register machines on natural numbers to machines whose registers contain arbitrary ordinals. Ordinal register machines are able to compute a recursive bounde...
We study Post’s Problem for the ordinal register machines defined in [6], showing that its general solution is positive, but that any set of ordinals solving it must be unbounde...
computability uses ordinals instead of natural numbers in abstract machines like register or Turing machines. We give an overview of the computational strengths of α-β-machines,...
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 quic...
Joel David Hamkins, David Linetsky, Russell G. Mil...
Abstract. Infinite time register machines (ITRMs) are register machines which act on natural numbers and which are allowed to run for arbitrarily many ordinal steps. Successor step...