Abstract: 

Raising to powers is an expansion of ACF proposed by Zilber. The idea is to construct the theory of the complex field expanded by "power functions" using the Hrushovski construction. Following his work, Bays, Kirby, and Gallinaro proved quasiminimality of this structure. In this talk, I will present my attempt to apply the Hrushovski construction to ordered fields — constructing a similar expansion of RCF that axiomatizes the real field with "power functions" on the unit circle. The resulting structure possesses, instead of quasiminimality, an o-minimal open core.

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