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...
Αποθηκεύτηκε σε:
| Κύριος συγγραφέας: | |
|---|---|
| Μορφή: | Livre numérique |
| Γλώσσα: | Anglais |
| Έκδοση: |
Berlin, Heidelberg :
Springer Berlin Heidelberg
[20..].
Cham : Springer Nature |
| Έκδοση: | 1st ed. 2009. |
| Σειρά: | Universitext
|
| Διαθέσιμο Online: | Accès sur la plateforme de l'éditeur Accès sur la plateforme Istex Accès Université d'Orléans Accès INSA CVL |
| Σημείωση: |
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 |
| LEADER | 04019nam a22004097a 4500 | ||
|---|---|---|---|
| 001 | 940971 | ||
| 008 | 090210q2000 xxe ||| |||| 00| 0 eng d | ||
| 009 | PPN131118528 | ||
| 020 | |a 9783540693192 | ||
| 041 | 0 | |a eng | |
| 082 | |a 511.3 | ||
| 084 | |a 03F03. 2000 | ||
| 084 | |a 03F05. 2000 | ||
| 084 | |a 03F15. 2000 | ||
| 100 | 1 | |a Pohlers, Wolfram. | |
| 245 | 1 | 0 | |a Proof theory : |b the first step into impredicativity |c by Wolfram Pohlers. |
| 250 | |a 1st ed. 2009. | ||
| 260 | |a Berlin, Heidelberg : |b Springer Berlin Heidelberg. | ||
| 260 | |a Cham : |b Springer Nature, |c [20..]. | ||
| 490 | 0 | |a Universitext |x 2191-6675 | |
| 500 | |a Description d'après consultation du 26 mars 2012 | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 500 | |a Archives Springer e-books (Licence nationale) | ||
| 504 | |a Bibliogr. Index | ||
| 505 | 1 | |a Historical Background Primitive Recursive Functions and Relations Ordinals Pure Logic Truth Complexity for ?11-Sentences Inductive Definitions The Ordinal Analysis for PA Autonomous Ordinals and the Limits of Predicativity Ordinal Analysis of the Theory for Inductive Definitions Provably Recursive Functions of NT Ordinal Analysis for Kripke Platek Set Theory with Infinity Predicativity Revisited Nonmonotone Inductive Definitions Epilogue | |
| 506 | |a Accès en ligne pour les établissements français bénéficiaires des licences nationales | ||
| 506 | |a Accès soumis à abonnement pour tout autre établissement | ||
| 506 | |a Conditions particulières de réutilisation pour les bénéficiaires des licences nationales. https://www.licencesnationales.fr/springer-nature-ebooks-contrat-licence-ln-2017 | ||
| 520 | |a 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 | ||
| 776 | 0 | |0 129758752 |t Proof theory |o the first step into impredicativity |f Wolfram Pohlers |c Berlin |n Springer |d 2009 |p 1 vol. (xiii-370 p.) |s Universitext |z 978-3-540-69318-5 | |
| 776 | 0 | |t Proof Theory |b Texte imprimé |z 9783540865322 | |
| 776 | 0 | |0 129758752 |t Proof theory |o the first step into impredicativity |f Wolfram Pohlers |c Berlin |n Springer |d 2009 |p 1 vol. (xiii-370 p.) |s Universitext |z 978-3-540-69318-5 | |
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| 856 | 4 | |5 180339901:750869518 |u https://ezproxy.insa-cvl.fr/login?qurl=https://dx.doi.org/10.1007/978-3-540-69319-2 |z Accès INSA CVL | |
| 997 | |0 940971 |1 Livre numérique |a Ressource numérique |b INSA |b ENSA |c 0/Bibliothèque numérique/ |c 1/Bibliothèque numérique/Autre ressource numérique/ | ||