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The Recognizability Strength of Infinite Time Turing Machines with Ordinal Parameters

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Unveiling Dynamics and Complexity (CiE 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10307))

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Abstract

We study infinite time Turing machines that attain a special state at a given class of ordinals during the computation. We prove results about sets that can be recognized by these machines. For instance, the recognizable sets of natural numbers with respect to the cardinal-detecting infinite time Turing machines introduced in [Hab13] are contained in a countable level of the constructible hierarchy, and the recognizable sets of natural numbers with respect to finitely many ordinal parameters are constructible.

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References

  1. Carl, M.: The distribution of \(ITRM\)-recognizable reals. Ann. Pure Appl. Logic 165(9), 1403–1417 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  2. Carl, M.: The lost melody phenomenon. In: Infinity, computability, and metamathematics, vol. 23 of Tributes, pp. 49–70. College Publications, London (2014)

    Google Scholar 

  3. Carl, M.: Optimal results on recognizability for infinite time register machines. J. Symb. Log. 80(4), 1116–1130 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Coskey, S., Hamkins, J.D.: Infinite time decidable equivalence relation theory. Notre Dame J. Formal Log. 52(2), 203–228 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  5. Carl, M., Schlicht, P.: Randomness via infinite time machines and effective descriptive set theory (2016). Submitted

    Google Scholar 

  6. Carl, M., Schlicht, P., Welch, P.: Recognizable sets and Woodin cardinals (2016). Submitted

    Google Scholar 

  7. Habič, M.E.: Cardinal-recognizing infinite time turing machines. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds.) CiE 2013. LNCS, vol. 7921, pp. 231–240. Springer, Heidelberg (2013). doi:10.1007/978-3-642-39053-1_27

    Chapter  Google Scholar 

  8. Hamkins, J.D., Lewis, A.: Infinite time turing machines. J. Symbolic Log. 65(2), 567–604 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Welch, P.D.: Minimality arguments for infinite time turing degrees. In: Sets and proofs (Leeds 1997). London Mathematical Society Lecture Note Series, vol. 258, pp. 425–436. Cambridge University Press, Cambridge (1999)

    Google Scholar 

  10. Welch, P.D.: Characteristics of discrete transfinite time Turing machine models: halting times, stabilization times, and normal form theorems. Theoret. Comput. Sci. 410(4–5), 426–442 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Welch, P.D.: Transfinite machine models. In: Turing’s Legacy: Developments from Turing’s Ideas in Logic. Lecture Notes in Logic, vol. 42, pp. 493–529. Association Symbolic Logic, La Jolla, CA (2014)

    Google Scholar 

  12. Zeman, M.: Inner Models and Large Cardinals. De Gruyter Series in Logic and its Applications, vol. 5. Walter de Gruyter & Co., Berlin (2012)

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik und Statistik, Universität Konstanz, Konstanz, Germany

    Merlin Carl & Philipp Schlicht

  2. Lehrstuhl für Theoretische Informatik, Universität Passau, Passau, Germany

    Merlin Carl & Philipp Schlicht

  3. Mathematisches Institut, Universität Bonn, Bonn, Germany

    Merlin Carl & Philipp Schlicht

Authors
  1. Merlin Carl
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  2. Philipp Schlicht
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Corresponding author

Correspondence to Merlin Carl .

Editor information

Editors and Affiliations

  1. University of Turku, Turku, Finland

    Jarkko Kari

  2. Christian-Albrechts-University of Kiel, Kiel, Germany

    Florin Manea

  3. Åbo Akademi University, Turku, Finland

    Ion Petre

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Carl, M., Schlicht, P. (2017). The Recognizability Strength of Infinite Time Turing Machines with Ordinal Parameters. In: Kari, J., Manea, F., Petre, I. (eds) Unveiling Dynamics and Complexity. CiE 2017. Lecture Notes in Computer Science(), vol 10307. Springer, Cham. https://doi.org/10.1007/978-3-319-58741-7_20

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  • DOI: https://doi.org/10.1007/978-3-319-58741-7_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-58740-0

  • Online ISBN: 978-3-319-58741-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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