Illinois Journal of Mathematics

o-minimal structures: low arity versus generation

Serge Randriambololona

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Abstract

We show that an analogue of Hilbert's Thirteenth Problem fails in the real subanalytic setting. Namely we prove that, for any integer $n$, the $o$-minimal structure generated by restricted analytic functions in $n$ variables is strictly smaller than the structure of all global subanalytic sets, whereas these two structures define the same subsets in $\mathbb{R}^{n+1}$.

Article information

Source
Illinois J. Math., Volume 49, Number 2 (2005), 547-558.

Dates
First available in Project Euclid: 13 November 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1258138034

Digital Object Identifier
doi:10.1215/ijm/1258138034

Mathematical Reviews number (MathSciNet)
MR2164352

Zentralblatt MATH identifier
1079.03027

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

Citation

Randriambololona, Serge. o-minimal structures: low arity versus generation. Illinois J. Math. 49 (2005), no. 2, 547--558. doi:10.1215/ijm/1258138034. https://projecteuclid.org/euclid.ijm/1258138034


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