Proof theory : the first step into impredicativity
This book verifies with compelling evidence the author s intent to "write a book on proof theory that needs no previous knowledge of proof theory". Avoiding the cryptic terminology of proof theory as far as possible, the book starts at an elementary level and displays the connections betwe...
Shranjeno v:
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| Format: | Livre numérique |
| Jezik: | Anglais |
| Izdano: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Izdaja: | 1st ed. 2009. |
| Serija: | Universitext
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| Online dostop: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Sporočilo: |
Description d'après consultation du 26 mars 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Autres localisations: | Voir dans le Sudoc |
| Edition sous un autre format: | • Proof theory, the first step into impredicativity, Wolfram Pohlers, Berlin, Springer, 2009, 1 vol. (xiii-370 p.), Universitext, 978-3-540-69318-5 • Proof Theory, Texte imprimé, 9783540865322 • Proof theory, the first step into impredicativity, Wolfram Pohlers, Berlin, Springer, 2009, 1 vol. (xiii-370 p.), Universitext, 978-3-540-69318-5 |
| Izvleček: | This book verifies with compelling evidence the author s intent to "write a book on proof theory that needs no previous knowledge of proof theory". Avoiding the cryptic terminology of proof theory as far as possible, the book starts at an elementary level and displays the connections between infinitary proof theory and generalized recursion theory, especially the theory of inductive definitions. As a "warm up" Gentzen's classical analysis of pure number theory is presented in a more modern terminology, followed by an explanation and proof of the famous result of Feferman and Schütte on the limits of predicativity. The author also provides an introduction to ordinal arithmetic, introduces the Veblen hierarchy and employs these functions to design an ordinal notation system for the ordinals below Epsilon 0 and Gamma 0, while emphasizing the first step into impredicativity, that is, the first step beyond Gamma 0. This is first done by an analysis of the theory of non-iterated inductive definitions using Buchholz s improvement of local predicativity, followed by Weiermann's observation that Buchholz s method can also be used for predicative theories to characterize their provably recursive functions. A second example presents an ordinal analysis of the theory of |
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| Opis knjige/članka: | Description d'après consultation du 26 mars 2012 Archives Springer e-books (Licence nationale) Archives Springer e-books (Licence nationale) |
| Bibliografija: | Bibliogr. Index |
| ISBN: | 9783540693192 |
| ISSN: | 2191-6675 |
| Dostop: | Accès en ligne pour les établissements français bénéficiaires des licences nationales Accès soumis à abonnement pour tout autre établissement Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 |