On Skolem's exponential functions below

Authors:
Lou van den Dries and Hilbert Levitz

Journal:
Trans. Amer. Math. Soc. **286** (1984), 339-349

MSC:
Primary 03D20; Secondary 06F05, 26A12

DOI:
https://doi.org/10.1090/S0002-9947-1984-0756043-7

MathSciNet review:
756043

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Abstract | References | Similar Articles | Additional Information

Abstract: A result of Ehrenfeucht implies that the smallest class of number-theoretic functions containing the constants , the identity function , and closed under addition, multiplication and , is well-ordered by the relation of eventual dominance. We show that its order type is , and that for any two nonzero functions in the class the quotient tends to a limit in as , where is the smallest set of positive real numbers containing and closed under addition, multiplication and under the operations .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1984-0756043-7

Article copyright:
© Copyright 1984
American Mathematical Society