Nagoya Mathematical Journal
- Nagoya Math. J.
- Volume 215 (2014), 225-237.
Two remarks on polynomially bounded reducts of the restricted analytic field with exponentiation
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.
Nagoya Math. J., Volume 215 (2014), 225-237.
First available in Project Euclid: 14 July 2014
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Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 03C64: Model theory of ordered structures; o-minimality
Secondary: 32B20: Semi-analytic sets and subanalytic sets [See also 14P15]
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