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Interpreting the projective hierarchy in expansions of the real line

Authors: Philipp Hieronymi and Michael Tychonievich
Journal: Proc. Amer. Math. Soc. 142 (2014), 3259-3267
MSC (2010): Primary 03C64
Published electronically: March 19, 2014
MathSciNet review: 3223381
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Abstract: We give a criterion when an expansion of the ordered set of real numbers defines the image of $ (\mathbb{R},+,\cdot ,\mathbb{N})$ under a semialgebraic injection. In particular, we show that for a non-quadratic irrational number $ \alpha $, the expansion of the ordered $ \mathbb{Q}(\alpha )$-vector space of real numbers by $ \mathbb{N}$ defines multiplication on $ \mathbb{R}$.

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Additional Information

Philipp Hieronymi
Affiliation: Department of Mathematics, University of Illinois at Urbana-Champaign, 1409 W. Green Street, Urbana, Illinois 61801

Michael Tychonievich
Affiliation: Department of Mathematics, The Ohio State University, 231 West 18th Avenue, Columbus, Ohio 43210

Received by editor(s): August 1, 2012
Received by editor(s) in revised form: September 13, 2012
Published electronically: March 19, 2014
Communicated by: Julia Knight
Article copyright: © Copyright 2014 American Mathematical Society

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