Mathematical Logic Quarterly 56 (5):503-507 (2010)

Abstract
The main goal of this note is to study for certain o-minimal structures the following propriety: for each definable C∞ function g0: [0, 1] → ℝ there is a definable C∞ function g: [–ε, 1] → ℝ, for some ε > 0, such that g = g0 for all x ∈ [0, 1]
Keywords Definability  o‐minimal structures
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DOI 10.1002/malq.200910105
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On the Elementary Theory of Restricted Elementary Functions.Lou van den Dries - 1988 - Journal of Symbolic Logic 53 (3):796 - 808.

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