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Logarithmic-Exponential Power Series |
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| Authors: | van den Dries Lou; Macintyre Angus; Marker David |
| Institution: | University of Illinois Urbana, Illinois 61801-2917, USA. E-mail: vddries{at}math.uiuc.edu Oxford University Oxford. E-mail: ajm{at}vax.ox.ac.uk Department of Mathematics, Statistics and Computer Science, The University of Illinois at Chicago Chicago, Illinois 60607-7045, USA. E-mail: marker{at}math.uic.edu |
| Abstract: | We use generalized power series to construct algebraically anonstandard model of the theory of the real field with exponentiation.This model enables us to show the undefinability of the zetafunction and certain non-elementary and improper integrals.We also use this model to answer a question of Hardy by showingthat the compositional inverse to the function (log x) (loglog x) is not asymptotic as x + to a composition of semialgebraicfunctions, log and exp. |
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