Journal of Symbolic Logic 76 (4):1418-1428 (2011)

Gareth Jones
Oxford Brookes University
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
Keywords real power functions   decidability   o-minimality
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DOI 10.2178/jsl/1318338857
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A Decision Method for Elementary Algebra and Geometry.Alfred Tarski - 1949 - Journal of Symbolic Logic 14 (3):188-188.
Expansions of the Real Field with Power Functions.Chris Miller - 1994 - Annals of Pure and Applied Logic 68 (1):79-94.

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