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NeuroCOLT
Technical Report NC-TR-98-013
Isomorphism Theorem for BSS Recursively
Enumerable Sets over Real Closed Fields
Christian Michaux & Christophe Troestler
Dept of Computer and Mathematics
University of Mons-Hainaut
Keywords:
Blum-Shub-Smale model; Recursively enumerable sets
Received:
10-JUN-98
Abstract
The main result of this paper lies in the
framework of BSS computability~: it shows roughly that any recursively
enumerable set $S$ in $R^N$, $N \le \infty$, where $R$ is a real closed
field, is isomorphic to $R^{\dim S}$ by a bijection $\phi$ which is
decidable over $S$. Moreover the map $S \To \phi$ is computable. Some
related matters are also considered like characterization of the real
closed fields with a r.e.\set of infinitesimals, and the dimension
of r.e.\ sets.
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