On skolem’s exponential functions below 22

Louvan Den Dries, Hilbert Levitz

Research output: Contribution to journalArticlepeer-review


A result of Ehrenfeucht implies that the smelliest class of number- theoretic functions(formula presented) containing the constants 0, 1, 2, the identity function X, and closed under addition, multiplication and(formula presented) c is well- ordered by the relation of eventual dominance. We show that its order type is (formula presented) c, and that for any two nonzero functions /, g in the class the quotient (formula presented) tends to a limit in E+ U{0, oo) as n(formula presented) c where E+ is the smallest set of positive real numbers containing 1 and closed under addition, multiplication and under the operations(formula presented).

Original languageEnglish (US)
Pages (from-to)339-349
Number of pages11
JournalTransactions of the American Mathematical Society
Issue number1
StatePublished - 1984
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics


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