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arXiv · 1303.4419

O-minimal structures: low arity versus generation

Serge Randriambololona
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Abstract

We show that an analogue of the 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 $\mathbb R ^{n+1}$.

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Serge Randriambololona. 2013-03-18. O-minimal structures: low arity versus generation. https://arxiv.org/abs/1303.4419

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