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 -