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

Abstract

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