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

Published online by Cambridge University Press:  12 March 2014

Ulrich Kohlenbach
Ulrich Kohlenbach*
Affiliation:
Fachbereich Mathematik, J.-W.-Goethe-Universität, W 6000 Frankfurt-Am-Main, Germany
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Abstract

We show how to extract effective bounds Φ for ⋀u1⋀v ≤ytu⋁wηG0-sentences which depend on u only (i.e. ⋀u⋀v ≤y, tu⋁w ≤η ΦuG0) from arithmetical proofs which use analytical assumptions of the form

(ϒ, 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

This is used to establish new conservation results about weak Konig's lemma. Applications to proofs in classical analysis, especially uniqueness proofs in approximation theory, will be given in subsequent papers.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 57 , Issue 4 , December 1992 , pp. 1239 - 1273
Copyright
Copyright © Association for Symbolic Logic 1992

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