Philipp Hieronymi, Michael Tychonievich
Published 2012-03-28, updated 2012-09-13Version 3
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.
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