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Computing a Model of Set Theory

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New Computational Paradigms (CiE 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3526))

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Abstract

We define the notion of ordinal computability by generalizing standard TURING computability on tapes of length ω to computations on tapes of arbitrary ordinal length. The generalized TURING machine is able to compute a recursive bounded truth predicate on the ordinals. The class of sets of ordinals which can be read off the truth predicate satisfies a natural theory SO. SO is the theory of the sets of ordinals in a model of the Zeremelo-Fraenkel axioms ZFC. Hence a set of ordinals is ordinal computable from ordinal parameters if and only if it is an element of GÖDEL’s constructible universe L.

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References

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Author information

Authors and Affiliations

  1. Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Beringstraße 1, 53113, Bonn, Germany

    Peter Koepke

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  1. Peter Koepke
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Editors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, U.K.

    S. Barry Cooper

  2. Department Mathematik, Universität Hamburg, Bundesstrasse 55, 20146, Hamburg, Germany

    Benedikt Löwe

  3. Universiteit van Amsterdam,  

    Leen Torenvliet

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© 2005 Springer-Verlag Berlin Heidelberg

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Koepke, P. (2005). Computing a Model of Set Theory. In: Cooper, S.B., Löwe, B., Torenvliet, L. (eds) New Computational Paradigms. CiE 2005. Lecture Notes in Computer Science, vol 3526. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11494645_28

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  • DOI: https://doi.org/10.1007/11494645_28

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-26179-7

  • Online ISBN: 978-3-540-32266-5

  • eBook Packages: Computer ScienceComputer Science (R0)

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