We show that the theory of the real field with a generic real power function is decidable, relative to an oracle for the rational cut of the exponent of the power function. We also show the existence of generic computable real numbers, hence providing an example of a decidable o-minimal proper expansion of the real field by an analytic function.
"On the decidability of the real field with a generic power function." J. Symbolic Logic 76 (4) 1418 - 1428, December 2011. https://doi.org/10.2178/jsl/1318338857