On the decidability of the real field with a generic power function

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

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10.2178/jsl/1318338857

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Gareth Jones
Oxford Brookes University

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Cardinal Algebras.Alfred Tarski & Bjarni Jonsson - 1949 - Journal of Symbolic Logic 14 (3):188-189.
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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