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

Published online by Cambridge University Press:  12 March 2014

Gareth Jones  and
Tamara Servi
Gareth Jones
Affiliation:
School of Mathematics, University of Manchester, Oxford Road, Manchester M13 9PL, UK, E-mail: Gareth.Jones-3@manchester.ac.uk
Tamara Servi
Affiliation:
Centro de Matemática e Aplicações Fundamentais, Av. Prof. Gama Pinto 2,1649-003 Lisboa, Portugal, E-mail: tamara.servi@googlemail.com
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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.

Keywords

real power functionsdecidabilityo-minimalityPrimary 03C6403B25
Type
Research Article
Information
The Journal of Symbolic Logic , Volume 76 , Issue 4 , December 2011 , pp. 1418 - 1428
Copyright
Copyright © Association for Symbolic Logic 2011

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References

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