aller au contenu
Proof theory : the first step into impredicativity Aperçu de cet ouvrage
FermerAperçu de cet ouvrage
Vérification...

Proof theory : the first step into impredicativity

Auteur : Wolfram Pohlers
Éditeur : New York ; London : Springer, ©2009.
Collection : Universitext.
Édition/format :   Livre électronique : Document : EnglishVoir toutes les éditions et tous les formats
Base de données :WorldCat
Résumé :
This book verifies with compelling evidence the author{u2019}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"  Lire la suite...
Évaluation :

(pas encore évalué) 0 avec des critiques - Soyez le premier.

Sujets
Plus comme ceci

 

Trouver un exemplaire en ligne

Liens vers cet ouvrage

Trouver un exemplaire dans la bibliothèque

&AllPage.SpinnerRetrieving; Recherche de bibliothèques qui possèdent cet ouvrage...

Détails

Genre/forme : Electronic books
Format – détails additionnels : Print version:
Pohlers, Wolfram.
Proof theory.
New York ; London : Springer, 2008
(OCoLC)233788989
Type d’ouvrage : Document, Ressource Internet
Format : Internet Resource, Computer File
Tous les auteurs / collaborateurs : Wolfram Pohlers
ISBN : 9783540693192 354069319X
Numéro OCLC : 310353075
Notes : Originally published: 1989.
Description : 1 online resource (xiii, 370 pages) : illustrations.
Contenu : 1 Historical Background --
2 Primitive Recursive Functions and Relations --
3 Ordinals --
4 Pure Logic --
5 Truth Complexities for Pi 1-1-Sentences --
6 Inductive Definitions --
7 The Ordinal Analysis for Pean Arithmetic --
8 Autonomous Ordinals and the Limits of Predicativity --
9 Ordinal Analysis of the Theory for Inductive Definitions --
10 Provably Recursive Functions of NT --
11 Ordinal Analysis for Kripke Platek Set Theory with infinity --
12 Predicativity Revisited --
13 Non-Monotone Inductive Definitions --
14 Epilogue.
Titre de collection : Universitext.
Responsabilité : by Wolfram Pohlers.

Résumé :

This book verifies with compelling evidence the author{u2019}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{u2019}s improvement of local predicativity, followed by Weiermann's observation that Buchholz{u2019}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 $/Pi_2$ reflection, a subsystem of set theory that is proof-theoretically equivalent to Kripke-Platek set. The book is pitched at undergraduate/graduate level, and thus addressed to students of mathematical logic interested in the basics of proof theory. It can be used for introductory as well as more advanced courses in proof theory. An earlier version of this book was published in 1989 as volume 1407 of the "Lecture Notes in Mathematics" (ISBN 978-3-540-51842-6).

Critiques

Critiques d’utilisateurs
Récupération des critiques de GoodReads...
Récuperation des critiques DOGObooks…

Étiquettes

Soyez le premier.

Ouvrages semblables

Sujets associés :(1)

Listes d’utilisateurs dans lesquelles cet ouvrage apparaît (1)

Confirmez cette demande

Vous avez peut-être déjà demandé cet ouvrage. Veuillez sélectionner OK si vous voulez poursuivre avec cette demande quand même.

Données liées


Primary Entity

<http://www.worldcat.org/oclc/310353075> # Proof theory : the first step into impredicativity
    a schema:MediaObject, schema:Book, schema:CreativeWork ;
    library:oclcnum "310353075" ;
    library:placeOfPublication <http://id.loc.gov/vocabulary/countries/nyu> ;
    library:placeOfPublication <http://dbpedia.org/resource/London> ; # London
    library:placeOfPublication <http://dbpedia.org/resource/New_York_City> ; # New York
    schema:about <http://id.worldcat.org/fast/1078942> ; # Proof theory
    schema:about <http://dewey.info/class/511.36/e22/> ;
    schema:bookFormat schema:EBook ;
    schema:copyrightYear "2009" ;
    schema:creator <http://viaf.org/viaf/25156760> ; # Wolfram Pohlers
    schema:datePublished "2009" ;
    schema:description "1 Historical Background -- 2 Primitive Recursive Functions and Relations -- 3 Ordinals -- 4 Pure Logic -- 5 Truth Complexities for Pi 1-1-Sentences -- 6 Inductive Definitions -- 7 The Ordinal Analysis for Pean Arithmetic -- 8 Autonomous Ordinals and the Limits of Predicativity -- 9 Ordinal Analysis of the Theory for Inductive Definitions -- 10 Provably Recursive Functions of NT -- 11 Ordinal Analysis for Kripke Platek Set Theory with infinity -- 12 Predicativity Revisited -- 13 Non-Monotone Inductive Definitions -- 14 Epilogue."@en ;
    schema:description "This book verifies with compelling evidence the author{u2019}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{u2019}s improvement of local predicativity, followed by Weiermann's observation that Buchholz{u2019}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 $/Pi_2$ reflection, a subsystem of set theory that is proof-theoretically equivalent to Kripke-Platek set. The book is pitched at undergraduate/graduate level, and thus addressed to students of mathematical logic interested in the basics of proof theory. It can be used for introductory as well as more advanced courses in proof theory. An earlier version of this book was published in 1989 as volume 1407 of the "Lecture Notes in Mathematics" (ISBN 978-3-540-51842-6)."@en ;
    schema:exampleOfWork <http://worldcat.org/entity/work/id/866283287> ;
    schema:genre "Electronic books"@en ;
    schema:inLanguage "en" ;
    schema:isPartOf <http://experiment.worldcat.org/entity/work/data/866283287#Series/universitext> ; # Universitext.
    schema:isSimilarTo <http://www.worldcat.org/oclc/233788989> ;
    schema:name "Proof theory : the first step into impredicativity"@en ;
    schema:productID "310353075" ;
    schema:publication <http://www.worldcat.org/title/-/oclc/310353075#PublicationEvent/new_york_london_springer_2009> ;
    schema:publisher <http://experiment.worldcat.org/entity/work/data/866283287#Agent/springer> ; # Springer
    schema:url <https://link.springer.com/openurl?genre=book&isbn=978-3-540-69318-5> ;
    schema:url <http://dx.doi.org/10.1007/978-3-540-69319-2> ;
    schema:workExample <http://worldcat.org/isbn/9783540693192> ;
    wdrs:describedby <http://www.worldcat.org/title/-/oclc/310353075> ;
    .


Related Entities

<http://dbpedia.org/resource/London> # London
    a schema:Place ;
    schema:name "London" ;
    .

<http://dbpedia.org/resource/New_York_City> # New York
    a schema:Place ;
    schema:name "New York" ;
    .

<http://experiment.worldcat.org/entity/work/data/866283287#Series/universitext> # Universitext.
    a bgn:PublicationSeries ;
    schema:hasPart <http://www.worldcat.org/oclc/310353075> ; # Proof theory : the first step into impredicativity
    schema:name "Universitext." ;
    schema:name "Universitext" ;
    .

<http://id.worldcat.org/fast/1078942> # Proof theory
    a schema:Intangible ;
    schema:name "Proof theory"@en ;
    .

<http://viaf.org/viaf/25156760> # Wolfram Pohlers
    a schema:Person ;
    schema:familyName "Pohlers" ;
    schema:givenName "Wolfram" ;
    schema:name "Wolfram Pohlers" ;
    .

<http://worldcat.org/isbn/9783540693192>
    a schema:ProductModel ;
    schema:isbn "354069319X" ;
    schema:isbn "9783540693192" ;
    .

<http://www.worldcat.org/oclc/233788989>
    a schema:CreativeWork ;
    rdfs:label "Proof theory." ;
    schema:description "Print version:" ;
    schema:isSimilarTo <http://www.worldcat.org/oclc/310353075> ; # Proof theory : the first step into impredicativity
    .


Content-negotiable representations

Fermer la fenêtre

Veuillez vous identifier dans WorldCat 

Dont have an account? You can easily créez un compte gratuit.