Light monotone Dialectica methods for proof mining
✍ Scribed by Mircea-Dan Hernest
- Publisher
- John Wiley and Sons
- Year
- 2009
- Tongue
- English
- Weight
- 150 KB
- Volume
- 55
- Category
- Article
- ISSN
- 0044-3050
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
In view of an enhancement of our implementation on the computer, we explore the possibility of an algorithmic optimization of the various proof‐theoretic techniques employed by Kohlenbach for the synthesis of new (and better) effective uniform bounds out of established qualitative proofs in Numerical Functional Analysis. Concretely, we prove that the method (developed by the author in his thesis, as an adaptation to Dialectica interpretations of Berger's original technique for modified realizability and A‐translation) of “colouring” some of the quantifiers as “non‐computational” extends well to ε‐arithmetization, elimination‐of‐extensionality and model‐interpretation (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)