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UNIFORM MODEL-COMPLETENESS FOR THE REAL FIELD EXPANDED BY POWER FUNCTIONS.
- Source :
- Journal of Symbolic Logic; Dec2010, Vol. 75 Issue 4, p1441-1461, 21p
- Publication Year :
- 2010
-
Abstract
- We prove that given any first order formula Φ in the language L' = {+, ⋅, <, (f<subscript>i</subscript>)<subscript>i∈I</subscript>, (c<subscript>i</subscript>)<subscript>i∈I</subscript>}, where the f<subscript>i</subscript> are unary function symbols and the c<subscript>i</subscript> are constants, one can find an existential formula ψ such that Φ and ψ are equivalent in any L'-structure 〈ℝ, +, ⋅, <, (x<superscript>c<subscript>i</subscript></superscript>)<subscript>i∈I</subscript>, (c<subscript>i</subscript>)<subscript>i∈I</subscript>〉. [ABSTRACT FROM AUTHOR]
- Subjects :
- FIRST-order logic
MATHEMATICAL functions
MATHEMATICAL logic
MODERN logic
MATHEMATICS
Subjects
Details
- Language :
- English
- ISSN :
- 00224812
- Volume :
- 75
- Issue :
- 4
- Database :
- Supplemental Index
- Journal :
- Journal of Symbolic Logic
- Publication Type :
- Academic Journal
- Accession number :
- 57214035
- Full Text :
- https://doi.org/10.2178/jsl/1286198156