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The Ordinal of Skolem + Tetration Is τ0

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

Abstract

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,

$$O(S_*,\,\preceq)=\tau_0,$$

is an immediate consequence.

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References

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    Barra, M., Gerhardy, P.: Skolem + Tetration is Well-Ordered. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds.) Mathematical Theory and Computational Practice. LNCS, vol. 5635, pp. 11–20. Springer, Heidelberg (2009)CrossRefGoogle Scholar
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    McBeth, R.: Exponential Polynomials of Linear Height. Zeitschr. f. math. Logik und Grundlagen d. Math. 26, 399–404 (1980)zbMATHCrossRefMathSciNetGoogle Scholar
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    Skolem, T.: An ordered set of arithmetic functions representing the least ε-number. Det Kongelige Norske Videnskabers selskabs Forhandlinger 29(12), 54–59 (1956)MathSciNetGoogle Scholar

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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