Post's Problem for Ordinal Register Machines

  • Authors:

  • Joel D. Hamkins;Russell G. Miller

  • Affiliations:

  • Department of Mathematics, College of Staten Island, and Doctoral Program in Mathematics, The CUNY Graduate Center,;Department of Mathematics, Queens College, and Doctoral Program in Computer Science, The CUNY Graduate Center,

  • Venue:
  • CiE '07 Proceedings of the 3rd conference on Computability in Europe: Computation and Logic in the Real World
  • Year:
  • 2007

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Abstract

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 unbounded in the writable ordinals. This mirrors the results in [3] for infinite-time Turing machines, and also provides insight into the different methods required for register machines and Turing machines in infinite time.