TY - JOUR
T1 - Interpreting the projective hierarchy in expansions of the real line
AU - Hieronymi, Philipp
AU - Tychonievich, Michael
N1 - Publisher Copyright:
© 2014 American Mathematical Society.
PY - 2014/9/1
Y1 - 2014/9/1
N2 - We give a criterion when an expansion of the ordered set of real numbers defines the image of (ℝ,+,·, ℕ) under a semialgebraic injection. In particular, we show that for a non-quadratic irrational number α, the expansion of the ordered ℚ(α)-vector space of real numbers by ℕ defines multiplication on ℝ.
AB - We give a criterion when an expansion of the ordered set of real numbers defines the image of (ℝ,+,·, ℕ) under a semialgebraic injection. In particular, we show that for a non-quadratic irrational number α, the expansion of the ordered ℚ(α)-vector space of real numbers by ℕ defines multiplication on ℝ.
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U2 - 10.1090/S0002-9939-2014-12023-5
DO - 10.1090/S0002-9939-2014-12023-5
M3 - Article
AN - SCOPUS:84924786994
SN - 0002-9939
VL - 142
SP - 3259
EP - 3267
JO - Proceedings of the American Mathematical Society
JF - Proceedings of the American Mathematical Society
IS - 9
ER -