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LOGARITHMIC-EXPONENTIAL POWER SERIES

Published online by Cambridge University Press:  01 December 1997

LOU VAN DEN DRIES ,
ANGUS MACINTYRE  and
DAVID MARKER
LOU VAN DEN DRIES
Affiliation:
University of Illinois, Urbana, Illinois 61801-2917, USA. E-mail: [email protected]
ANGUS MACINTYRE
Affiliation:
Oxford University, Oxford. E-mail: [email protected]
DAVID MARKER
Affiliation:
Department of Mathematics, Statistics and Computer Science, The University of Illinois at Chicago, Chicago, Illinois 60607-7045, USA. E-mail: [email protected]
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Abstract

We use generalized power series to construct algebraically a nonstandard model of the theory of the real field with exponentiation. This model enables us to show the undefinability of the zeta function and certain non-elementary and improper integrals. We also use this model to answer a question of Hardy by showing that the compositional inverse to the function (log x) (log log x) is not asymptotic as x→+∞ to a composition of semialgebraic functions, log and exp.

Type
Notes and Papers
Information
Journal of the London Mathematical Society , Volume 56 , Issue 3 , December 1997 , pp. 417 - 434
Copyright
The London Mathematical Society 1997

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