Interpreting the projective hierarchy in expansions of the real line

Details Interpreting the projective hierarchy in expansions of the real line Interpreting the projective hierarchy in expansions of the real line

2012-03-28

arxiv.org/abs/1203.6299v1

Mathematics

Logic

Scientific paper

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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