Proof mining in L1-approximation
Ulrich Kohlenbach,Paulo Oliva +1 more
TL;DR: The result of the analysis of Cheney's proof provides the first effective (in all parameters) uniform modulus of uniqueness (a concept which generalizes ‘strong uniqueness’ studied extensively in approximation theory).
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About: This article is published in Annals of Pure and Applied Logic. The article was published on 15 May 2003. and is currently open access. The article focuses on the topics: Proof mining & Proof theory.
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Citations
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Proofs and Computations
Helmut Schwichtenberg,Stanley S. Wainer +1 more
- 01 Dec 2011
TL;DR: This book provides a unique self-contained text for advanced students and researchers in mathematical logic and computer science and develops the theoretical underpinnings of the first author's proof assistant MINLOG.
A complexity analysis of functional interpretations
TL;DR: A quantitative analysis of Godel's functional interpretation and its monotone variant is given and upper bounds in basic proof data are given on the depth, size, maximal type degree and maximal type arity of the extracted terms as well as on the Depth of the verifying proof.
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Effective Uniform Bounds from Proofs in Abstract Functional Analysis
Ulrich Kohlenbach
- 01 Jan 2008
TL;DR: Proof mining as discussed by the authors is a technique for transforming prima facie ineffective proofs into proofs from which certain quantitative computational information as well as new qualitative information can be read off which was not visible beforehand.
An Analysis of Gödel's dialectica Interpretation via Linear Logic
TL;DR: In this article, an analysis of Godel's dialectica interpretation via a refinement of intuitionistic logic known as linear logic is presented, where the role of contraction in extensions to classical logic, arithmetic and analysis is also discussed.
A complexity analysis of functional interpretations
Mircea Dan Hernest,Ulrich Kohlenbach +1 more
TL;DR: A quantitative analysis of Godel's functional interpretation and its monotone variant is given and upper bounds in basic proof data are given on the depth, size, maximal type degree and maximal type arity of the extracted terms as well as on the Depth of the verifying proof.
17
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Metamathematical investigation of intuitionistic arithmetic and analysis
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