UNIFORM MODEL-COMPLETENESS FOR THE REAL FIELD EXPANDED BY POWER FUNCTIONS.

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〉. [ABSTRACT FROM AUTHOR]