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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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.

Article information

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

Dates
First available in Project Euclid: 11 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1318338857

Digital Object Identifier
doi:10.2178/jsl/1318338857

Mathematical Reviews number (MathSciNet)
MR2895403

Zentralblatt MATH identifier
1261.03123

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

Keywords
real power functions decidability o-minimality

Citation

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. https://projecteuclid.org/euclid.jsl/1318338857


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