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Admissibles in Gaps

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2017

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Durand, Bruno
Lafitte, Grégory
Ouazzani, Sabrina

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https://doi.org/10.1007/978-3-319-58741-7_18
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KARI, Jarkko, ed. and others. Unveiling Dynamics and Complexity : 13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017, Proceedings. Cham: Springer, 2017, pp. 175-186. Lecture Notes in Computer Science. 10307. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-319-58740-0. Available under: doi: 10.1007/978-3-319-58741-7_18

Zusammenfassung

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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510 Mathematik

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13th Conference on Computability in Europe, CiE 2017, 12. Juni 2017 - 16. Juni 2017, Turku, Finland
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ISO 690CARL, Merlin, Bruno DURAND, Grégory LAFITTE, Sabrina OUAZZANI, 2017. Admissibles in Gaps. 13th Conference on Computability in Europe, CiE 2017. Turku, Finland, 12. Juni 2017 - 16. Juni 2017. In: KARI, Jarkko, ed. and others. Unveiling Dynamics and Complexity : 13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017, Proceedings. Cham: Springer, 2017, pp. 175-186. Lecture Notes in Computer Science. 10307. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-319-58740-0. Available under: doi: 10.1007/978-3-319-58741-7_18
BibTex
@inproceedings{Carl2017-05-12Admis-41574,
  year={2017},
  doi={10.1007/978-3-319-58741-7_18},
  title={Admissibles in Gaps},
  number={10307},
  isbn={978-3-319-58740-0},
  issn={0302-9743},
  publisher={Springer},
  address={Cham},
  series={Lecture Notes in Computer Science},
  booktitle={Unveiling Dynamics and Complexity : 13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017, Proceedings},
  pages={175--186},
  editor={Kari, Jarkko},
  author={Carl, Merlin and Durand, Bruno and Lafitte, Grégory and Ouazzani, Sabrina}
}
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