TY - JOUR

T1 - On skolem’s exponential functions below 22

AU - Den Dries, Louvan

AU - Levitz, Hilbert

N1 - Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1984

Y1 - 1984

N2 - 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).

AB - 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).

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U2 - 10.1090/S0002-9947-1984-0756043-7

DO - 10.1090/S0002-9947-1984-0756043-7

M3 - Article

AN - SCOPUS:84968480588

VL - 286

SP - 339

EP - 349

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 1

ER -