Journal of Symbolic Logic

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

Gareth Jones and Tamara Servi

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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.

Article information

J. Symbolic Logic, Volume 76, Issue 4 (2011), 1418-1428.

First available in Project Euclid: 11 October 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 03C64: Model theory of ordered structures; o-minimality 03B25: Decidability of theories and sets of sentences [See also 11U05, 12L05, 20F10]

real power functions decidability o-minimality


Jones, Gareth; Servi, Tamara. On the decidability of the real field with a generic power function. J. Symbolic Logic 76 (2011), no. 4, 1418--1428. doi:10.2178/jsl/1318338857.

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