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Post’s Problem for Ordinal Register Machines

  • Joel D. Hamkins
  • Russell G. Miller
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4497)

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.

Keywords

computability ordinal computability ordinal register machine Post’s Problem 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Joel D. Hamkins
    • 1
  • Russell G. Miller
    • 2
  1. 1.Department of Mathematics, College of Staten Island, and Doctoral Program in Mathematics, The CUNY Graduate CenterUSA
  2. 2.Department of Mathematics, Queens College, and Doctoral Program in Computer Science, The CUNY Graduate CenterUSA

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