The Set of Restricted Complex Exponents for Expansions of the Reals

Notre Dame Journal of Formal Logic 53 (2):175-186 (2012)
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Abstract

We introduce the set of definable restricted complex powers for expansions of the real field and calculate it explicitly for expansions of the real field itself by collections of restricted complex powers. We apply this computation to establish a classification theorem for expansions of the real field by families of locally closed trajectories of linear vector fields

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10.1215/00294527-1715671

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Expansions of the real field with power functions.Chris Miller - 1994 - Annals of Pure and Applied Logic 68 (1):79-94.
Undefinability results in o-minimal expansions of the real numbers.Ricardo Bianconi - 2005 - Annals of Pure and Applied Logic 134 (1):43-51.

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