Real Algebraic and Analytic Geometry

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122. Serge Randriambololona:
O-minimal structures: low arity versus generation.


Submission: 2004, June 30.

We prove that an analogue of the Hilbert's Thirteenth Problem fails in the real subanalytic setting. Namely we show 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 R ^{n+1}.

Mathematics Subject Classification (2000): 03C64, 26B40, 32B20, 32A05.

Keywords and Phrases: o-minimal structure, global subanalytic sets, formal series, representation of functions.

Full text, 11p.: dvi 51k, ps.gz 169k, pdf 250k.

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