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Higher Type Recursion for Transfinite Machine Theory

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Computing with Foresight and Industry (CiE 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11558))

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Abstract

We look at some preliminary work in the theory of transfinite Turing machines generalised in the manner of Kleene to higher type recursion theory. The underlying philosophy is that ordinary Turing computability and inductive definability is replaced by the example here of Infinite Time Turing Machine computability and quasi-inductive definability.

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Authors and Affiliations

  1. School of Mathematics, University of Bristol, Bristol, BS8 1TW, England

    Philip Welch

Authors
  1. Philip Welch
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Correspondence to Philip Welch .

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Editors and Affiliations

  1. Christian Albrechts University of Kiel, Kiel, Germany

    Florin Manea

  2. Durham University, Durham, UK

    Barnaby Martin

  3. Durham University, Durham, UK

    Daniël Paulusma

  4. Università degli Studi di Milano, Milan, Italy

    Giuseppe Primiero

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Welch, P. (2019). Higher Type Recursion for Transfinite Machine Theory. In: Manea, F., Martin, B., Paulusma, D., Primiero, G. (eds) Computing with Foresight and Industry. CiE 2019. Lecture Notes in Computer Science(), vol 11558. Springer, Cham. https://doi.org/10.1007/978-3-030-22996-2_7

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  • DOI: https://doi.org/10.1007/978-3-030-22996-2_7

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-22995-5

  • Online ISBN: 978-3-030-22996-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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