Undefinability results in o-minimal expansions of the real numbers

Annals of Pure and Applied Logic 134 (1):43-51 (2005)
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Abstract

We show that if is not in the field generated by α1,…,αn, then no restriction of the function xβ to an interval is definable in . We also prove that if the real and imaginary parts of a complex analytic function are definable in Rexp or in the expansion of by functions xα, for irrational α, then they are already definable in . We conclude with some conjectures and open questions

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DOI

10.1016/j.apal.2004.06.010

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Citations of this work

R-analytic functions.Tobias Kaiser - 2016 - Archive for Mathematical Logic 55 (5-6):605-623.

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References found in this work

Expansions of the real field with power functions.Chris Miller - 1994 - Annals of Pure and Applied Logic 68 (1):79-94.
Tame Topology and O-Minimal Structures.Lou van den Dries - 2000 - Bulletin of Symbolic Logic 6 (2):216-218.

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