Nagoya Mathematical Journal

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

Serge Randriambololona

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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.

Article information

Source
Nagoya Math. J., Volume 215 (2014), 225-237.

Dates
First available in Project Euclid: 14 July 2014

Permanent link to this document
https://projecteuclid.org/euclid.nmj/1405342240

Digital Object Identifier
doi:10.1215/00277630-2781221

Mathematical Reviews number (MathSciNet)
MR3263529

Zentralblatt MATH identifier
1306.81217

Subjects
Primary: 03C64: Model theory of ordered structures; o-minimality
Secondary: 32B20: Semi-analytic sets and subanalytic sets [See also 14P15]

Citation

Randriambololona, Serge. Two remarks on polynomially bounded reducts of the restricted analytic field with exponentiation. Nagoya Math. J. 215 (2014), 225--237. doi:10.1215/00277630-2781221. https://projecteuclid.org/euclid.nmj/1405342240


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