Effective Bounds from ineffective proofs in analysis: An application of functional interpretation and majorization

Journal of Symbolic Logic 57 (4):1239-1273 (1992)
We show how to extract effective bounds Φ for $\bigwedge u^1 \bigwedge v \leq_\gamma tu \bigvee w^\eta G_0$ -sentences which depend on u only (i.e. $\bigwedge u \bigwedge v \leq_\gamma tu \bigvee w \leq_\eta \Phi uG_0$ ) from arithmetical proofs which use analytical assumptions of the form \begin{equation*}\tag{*}\bigwedge x^\delta\bigvee y \leq_\rho sx \bigwedge z^\tau F_0\end{equation*} (γ, δ, ρ, and τ are arbitrary finite types, η ≤ 2, G0 and F0 are quantifier-free, and s and t are closed terms). If τ ≤ 2, (*) can be weakened to $\bigwedge x^\delta, z^\tau\bigvee y \leq_\rho sx \bigwedge \tilde{z} \leq_\tau z F_0$ . This is used to establish new conservation results about weak König's lemma. Applications to proofs in classical analysis, especially uniqueness proofs in approximation theory, will be given in subsequent papers
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DOI 10.2307/2275367
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References found in this work BETA
Fragments of Arithmetic.Wilfried Sieg - 1983 - Annals of Pure and Applied Logic 28 (1):33-71.
Pointwise Hereditary Majorization and Some Applications.Ulrich Kohlenbach - 1992 - Archive for Mathematical Logic 31 (4):227-241.
Herbrand Analyses.Wilfried Sieg - 1991 - Archive for Mathematical Logic 30 (5-6):409-441.
On Some Formalized Conservation Results in Arithmetic.P. Clote, P. Hájek & J. Paris - 1990 - Archive for Mathematical Logic 30 (4):201-218.

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Bounded Functional Interpretation.Fernando Ferreira & Paulo Oliva - 2005 - Annals of Pure and Applied Logic 135 (1):73-112.

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