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,
is an immediate consequence.
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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)
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)
McBeth, R.: Exponential Polynomials of Linear Height. Zeitschr. f. math. Logik und Grundlagen d. Math. 26, 399–404 (1980)
Sierpiński, W.: Cardinal and Ordinal Numbers. PWN-Polish Scientific Publishers, Warszawa (1965)
Skolem, T.: An ordered set of arithmetic functions representing the least ε-number. Det Kongelige Norske Videnskabers selskabs Forhandlinger 29(12), 54–59 (1956)
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Barra, M., Gerhardy, P. (2010). The Ordinal of Skolem + Tetration Is τ 0 . In: Ferreira, F., Löwe, B., Mayordomo, E., Mendes Gomes, L. (eds) Programs, Proofs, Processes. CiE 2010. Lecture Notes in Computer Science, vol 6158. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13962-8_4
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DOI: https://doi.org/10.1007/978-3-642-13962-8_4
Publisher Name: Springer, Berlin, Heidelberg
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