# Expansions of the Real Field with Power Functions

@article{Miller1994ExpansionsOT, title={Expansions of the Real Field with Power Functions}, author={Chris Miller}, journal={Ann. Pure Appl. Log.}, year={1994}, volume={68}, pages={79-94} }

Abstract We investigate expansions of the ordered field of real numbers equipped with a family of real power functions. We show in particular that the (O-minimal) theory of the ordered field of real numbers augmented by all restricted analytic functions and all real power functions admits elimination of quantifiers and has a universal axiomatization. We derive that every function of one variable definable in this structure, not ultimately identically 0, is asymptotic at + ∞ to a real function… Expand

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