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Admissibles in Gaps

  • Merlin CarlEmail author
  • Bruno DurandEmail author
  • Grégory LafitteEmail author
  • Sabrina Ouazzani
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10307)

Abstract

We consider clockable ordinals for Infinite Time Turing Machines (ITTMs), i.e., halting times of ITTMs on the empty input. It is well-known that, in contrast to the writable ordinals, the set of clockable ordinals has ‘gaps’. In this paper, we show several results on gaps, mainly related to the admissible ordinals they may properly contain. We prove that any writable ordinal can occur as the order type of the sequence of admissible ordinals in such a gap. We give precise information on their ending points. We also investigate higher rank ordinals (recursively inaccessible, etc.). Moreover, we show that those gaps can have any reasonably effective length (in the sense of ITTMs) compared to their starting point.

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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Fachbereich Mathematik und StatistikUniversität KonstanzKonstanzGermany
  2. 2.Lehrstuhl für Theoretische InformatikUniversität PassauPassauGermany
  3. 3.LIRMM, CNRS, Université de MontpellierMontpellierFrance
  4. 4.LACL, Université Paris-EstCréteilFrance

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