omitir hasta el contenido
Proof theory : the first step into impredicativity Ver este material de antemano
CerrarVer este material de antemano
Chequeando…

Proof theory : the first step into impredicativity

Autor: Wolfram Pohlers
Editorial: New York ; London : Springer, ©2009.
Serie: Universitext.
Edición/Formato:   Libro-e : Documento : Inglés (eng)Ver todas las ediciones y todos los formatos
Base de datos:WorldCat
Resumen:
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"  Leer más
Calificación:

(todavía no calificado) 0 con reseñas - Ser el primero.

Temas
Más materiales como éste

 

Encontrar un ejemplar en línea

Enlaces a este material

Encontrar un ejemplar en la biblioteca

&AllPage.SpinnerRetrieving; Encontrando bibliotecas que tienen este material…

Detalles

Género/Forma: Electronic books
Formato físico adicional: Print version:
Pohlers, Wolfram.
Proof theory.
New York ; London : Springer, 2008
(OCoLC)233788989
Tipo de material: Documento, Recurso en Internet
Tipo de documento: Recurso en Internet, Archivo de computadora
Todos autores / colaboradores: Wolfram Pohlers
ISBN: 9783540693192 354069319X
Número OCLC: 310353075
Notas: Originally published: 1989.
Descripción: 1 online resource (xiii, 370 pages) : illustrations.
Contenido: 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.
Título de la serie: Universitext.
Responsabilidad: by Wolfram Pohlers.

Resumen:

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).

Reseñas

Reseñas contribuidas por usuarios
Recuperando reseñas de GoodReads…
Recuperando reseñas de DOGObooks…

Etiquetas

Ser el primero.

Materiales similares

Temas relacionados:(1)

Listas de usuarios con este material (1)

Confirmar este pedido

Ya ha pedido este material. Escoja OK si desea procesar el pedido de todos modos.

Datos enlazados


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

Cerrar ventana

Inicie una sesión con WorldCat 

¿No tienes una cuenta? Puede fácilmente crear una cuenta gratuita.