The Ordinal of Skolem + Tetration Is τ0

  • Mathias Barra
  • Philipp Gerhardy
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6158)


In [1], we proved that a certain family of number theoretic functions S * is well-ordered by the majorisation relation ‘≼’. Furthermore, we proved that a lower bound on the ordinal O(S *, ≼ ) of this well-order is the least critical epsilon number τ 0. In this paper we prove that τ 0 is also an upper bound for its ordinal, whence our sought-after result,


is an immediate consequence.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

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

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