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On the Extraction of Computational Content from Noneffective Convergence Proofs in Analysis
Annotation
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Berlin :
Logos Verlag Berlin,
2014.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Intro; 1 Preliminaries; 1.1 The System WE-HAw; 1.2 Fragments and Extensions of WE-HAw; 1.3 The ordered Field of rational Numbers within WE-HAw; 1.4 The Archimedean ordered Field of real Numbers within WE-HAw; 1.5 Kuroda's negative Translation; 1.6 Gödel's Functional Interpretation; 1.7 Majorizability; 1.8 Monotone Functional Interpretation; 1.9 A specific metatheorem; 1.10 Models of E-PAw; 1.11 Bar Recursion; 1.12 Law of excluded Middle; 1.13 Double Negation Shift; 1.14 Axiom of Choice; 1.15 Arithmetical Comprehension; 1.16 Weak König's Lemma; 1.17 Complexity classes and bar recursion
- 2 Effective learnability2.1 Fluctuations versus effective learnability; 2.2 Cauchy statements and unrestricted use of S01-LEM; 2.3 Which Cauchy statements are effectively learnable and which are not; 2.4 When learnability implies fluctuation bounds; 3 Interpreting a strong non-linear ergodic theorem; 3.1 Arithmetizing Wittmann's proof; 3.2 Obtaining a bound; 3.3 A general bound existence theorem; 3.4 Uniform bounds for Wittmann's ergodic theorems; 3.5 Proof of Proposition 3.9; 4 Interpreting Bolzano-Weierstraß; 4.1 Interpreting Bolzano-Weierstraß
- 4.2 Analysis of the Complexity of the Realizers5 Functional interpretation for IST; 5.1 Formalities; 5.2 Nonstandard principles; 5.3 A functional interpretation for E-HA; 5.4 The system E-PA and negative translation; 5.5 A functional interpretation for E-PA; 5.6 Countable saturation