o-minimal structures: low arity versus generation
Randriambololona, Serge
Illinois J. Math., Tome 49 (2005) no. 2, p. 547-558 / Harvested from Project Euclid
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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 $\mathbb{R}^{n+1}$.
Publié le : 2005-04-15
Classification:  03C64,  32B20 
@article{1258138034,
     author = {Randriambololona, Serge},
     title = {o-minimal structures: low arity versus generation},
     journal = {Illinois J. Math.},
     volume = {49},
     number = {2},
     year = {2005},
     pages = { 547-558},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1258138034}
}

Randriambololona, Serge. o-minimal structures: low arity versus generation. Illinois J. Math., Tome 49 (2005) no. 2, pp.  547-558. http://gdmltest.u-ga.fr/item/1258138034/