Journal of Symbolic Logic

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

Tom Foster

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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

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

First available in Project Euclid: 4 October 2010

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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