Applied Proof Theory: Proof Interpretations and their Use in Mathematics
Ulrich Kohlenbach presents an applied form of proof theory that has led in recent years to new results in number theory, approximation theory, nonlinear analysis, geodesic geometry and ergodic theory (among others). This applied approach is based on logical transformations (so-called proof interpret...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
2008, 2008
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| Edition: | 1st ed. 2008 |
| Series: | Springer Monographs in Mathematics
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| Subjects: | |
| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- Unwinding proofs (‘Proof Mining’)
- Intuitionistic and classical arithmetic in all finite types
- Representation of Polish metric spaces
- Modified realizability
- Majorizability and the fan rule
- Semi-intuitionistic systems and monotone modified realizability
- Gödel’s functional (‘Dialectica’) interpretation
- Semi-intuitionistic systems and monotone functional interpretation
- Systems based on classical logic and functional interpretation
- Functional interpretation of full classical analysis
- A non-standard principle of uniform boundedness
- Elimination of monotone Skolem functions
- The Friedman A-translation
- Applications to analysis: general metatheorems I
- Case study I: Uniqueness proofs in approximation theory
- Applications to analysis: general metatheorems II
- Case study II: Applications to the fixed point theory of nonexpansive mappings
- Final comments