The Ordinal of Skolem + Tetration Is τ0
In , 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.
Unable to display preview. Download preview PDF.
- 2.Lebitz, H.: An ordered set of Arithmetic Functions Representing the Least ε-number. Zeitschr. f. math. Logik und Grundlagen d. Math. 21, 115–120 (1975)Google Scholar