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Two remarks on polynomially bounded reducts of the restricted analytic field with exponentiation

Published online by Cambridge University Press:  11 January 2016

Serge Randriambololona
Serge Randriambololona*
Affiliation:
Galatasaray Ünivertisesi, Matematik Bölümü, Örtaköy/Istanbul, Turkey, serge.randriambololona@ens-lyon.org, serge.randriambololona@math.cnrs.fr
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Abstract

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This article presents two constructions motivated by a conjecture of van den Dries and Miller concerning the restricted analytic field with exponentiation. The first construction provides an example of two o-minimal expansions of a real closed field that possess the same field of germs at infinity of one-variable functions and yet define different global one-variable functions. The second construction gives an example of a family of infinitely many distinct maximal polynomially bounded reducts (all this in the sense of definability) of the restricted analytic field with exponentiation.

Keywords

03C6432B20
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 215 , September 2014 , pp. 225 - 237
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2014

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