TWO REMARKS ON POLYNOMIALLY BOUNDED REDUCTS OF THE RESTRICTED ANALYTIC FIELD WITH EXPONENTIATION
NAGOYA MATHEMATICAL JOURNAL, vol.215, pp.225-237, 2014 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 215
- Publication Date: 2014
- Doi Number: 10.1215/00277630-2781221
- Journal Name: NAGOYA MATHEMATICAL JOURNAL
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.225-237
- Open Archive Collection: AVESIS Open Access Collection
- Galatasaray University Affiliated: No
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.