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Preprint Number 569

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569. Serge Randriambololona
Two remarks on polynomially bounded reducts of the restricted analytic field with exponentiation
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18 March 2013.

Abstract:

This article presents two constructions motivated by a conjecture of L. van den Dries and C. Miller concerning the restricted analytic field with exponentiation. The first construction provides an example of two o-minimal expansions of a real closed field that possess the same field of germs at infinity of one-variable functions and yet define different global one-variable functions. The second construction gives an example of a family of infinitely many distinct polynomially bounded reducts (all this in the sense of definability) of the restricted analytic field with exponentiation.

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Full text arXiv 1303.4407: pdf, ps.


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