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

TOM FOSTER
The Journal of Symbolic Logic
Vol. 75, No. 4 (DECEMBER 2010), pp. 1441-1461
Stable URL: http://www.jstor.org/stable/20799324
Page Count: 21
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## 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 $\langle {\Bbb R},+,.,<,(x^{c_{i}})_{i\in I},(c_{i})_{i\in I}\rangle$ .

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