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Preprint Number 433

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433. Philipp Hieronymi, Michael Tychonievich
Interpreting the projective hierarchy in expansions of the real line

Submission date: 29 March 2012.


We give a criterion when an expansion of the ordered set of real numbers defines the image of the expansion of the real field by the set of natural numbers under a semialgebraic injection. In particular, we show that for a non-quadratic irrational number a, the expansion of the ordered Q(a)-vector space of real numbers by the set of natural numbers defines multiplication on the real numbers.

Mathematics Subject Classification: 03C64

Keywords and phrases:

Full text arXiv 1203.6299: pdf, ps.

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