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

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

#### 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〉.

First Page:
Primary Subjects: 03C64
Secondary Subjects: 03C10
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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

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