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Skolem + Tetration Is Well-Ordered

  • Mathias Barra
  • Philipp Gerhardy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5635)

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Mathias Barra
    • 1
  • Philipp Gerhardy
    • 1
  1. 1.Dept. of MathematicsUniversity of OsloOsloNorway

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