TWO REMARKS ON POLYNOMIALLY BOUNDED REDUCTS OF THE RESTRICTED ANALYTIC FIELD WITH EXPONENTIATION


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Randriambololona S.

NAGOYA MATHEMATICAL JOURNAL, vol.215, pp.225-237, 2014 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 215
  • Publication Date: 2014
  • Doi Number: 10.1215/00277630-2781221
  • Title of Journal : NAGOYA MATHEMATICAL JOURNAL
  • Page Numbers: pp.225-237

Abstract

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.