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Skolem + Tetration Is Well-Ordered

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Mathematical Theory and Computational Practice (CiE 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5635))

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Abstract

The problem of whether a certain set of number-theoretic functions – defined via tetration (i.e. iterated exponentiation) – is well-ordered by the majorisation relation, was posed by Skolem in 1956. We prove here that indeed it is a computable well-order, and give a lower bound τ 0 on its ordinal.

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Authors and Affiliations

  1. Dept. of Mathematics, University of Oslo, P.B. 1053, Blindern, 0316, Oslo, Norway

    Mathias Barra & Philipp Gerhardy

Authors
  1. Mathias Barra
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  2. Philipp Gerhardy
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Editors and Affiliations

  1. University of Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    Klaus Ambos-Spies

  2. Universiteit van Amsterdam, Plantage Muidergracht 24, 1018, Amsterdam, TV, The Netherlands

    Benedikt Löwe

  3. Institut für Informatik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 294, 69120, Heidelberg, Germany

    Wolfgang Merkle

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© 2009 Springer-Verlag Berlin Heidelberg

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Barra, M., Gerhardy, P. (2009). Skolem + Tetration Is Well-Ordered. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds) Mathematical Theory and Computational Practice. CiE 2009. Lecture Notes in Computer Science, vol 5635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03073-4_2

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  • DOI: https://doi.org/10.1007/978-3-642-03073-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03072-7

  • Online ISBN: 978-3-642-03073-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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