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Preprint Number 227

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227. Gareth Jones, Tamara Servi
On the decidability of the real field with a generic power function

Submission date: 25 January 2010.


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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