Journal of Symbolic Logic

Uniform model-completeness for the real field expanded by power functions

Tom Foster

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Abstract

We prove that given any first order formula φ in the language L'={+,·, <, (fi)i ∈ I,(ci)i ∈ I}, where the fi are unary function symbols and the ci are constants, one can find an existential formula ψ such that φ and ψ are equivalent in any L'-structure 〈ℝ,+,·, <,(xci)i ∈ I,(ci)i ∈ I〉.

Article information

Source
J. Symbolic Logic Volume 75, Issue 4 (2010), 1441-1461.

Dates
First available in Project Euclid: 4 October 2010

Permanent link to this document
http://projecteuclid.org/euclid.jsl/1286198156

Digital Object Identifier
doi:10.2178/jsl/1286198156

Zentralblatt MATH identifier
05835175

Mathematical Reviews number (MathSciNet)
MR2767978

Subjects
Primary: 03C64: Model theory of ordered structures; o-minimality
Secondary: 03C10: Quantifier elimination, model completeness and related topics

Citation

Foster, Tom. Uniform model-completeness for the real field expanded by power functions. J. Symbolic Logic 75 (2010), no. 4, 1441--1461. doi:10.2178/jsl/1286198156. http://projecteuclid.org/euclid.jsl/1286198156.


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