Submission date: 25 January 2010.

Abstract:

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 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.

Mathematics Subject Classification: 03C64; 03B25

Keywords and phrases: real power functions; decidability; o-minimality.

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