The Resource Proof theory : the first step into impredicativity, Wolfram Pohlers
Proof theory : the first step into impredicativity, Wolfram Pohlers
Resource Information
The item Proof theory : the first step into impredicativity, Wolfram Pohlers represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Proof theory : the first step into impredicativity, Wolfram Pohlers represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Missouri Libraries.
This item is available to borrow from 1 library branch.
 Summary
 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 noniterated 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 $/Pi_2$ reflection, a subsystem of set theory that is prooftheoretically equivalent to KripkePlatek 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 9783540518426)
 Language
 eng
 Extent
 1 online resource (xiii, 370 pages).
 Contents

 1 Historical Background
 2 Primitive Recursive Functions and Relations
 3 Ordinals
 4 Pure Logic
 5 Truth Complexities for Pi 11Sentences
 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 NonMonotone Inductive Definitions
 14 Epilogue
 Isbn
 9783540693192
 Label
 Proof theory : the first step into impredicativity
 Title
 Proof theory
 Title remainder
 the first step into impredicativity
 Statement of responsibility
 Wolfram Pohlers
 Language
 eng
 Summary
 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 noniterated 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 $/Pi_2$ reflection, a subsystem of set theory that is prooftheoretically equivalent to KripkePlatek 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 9783540518426)
 Cataloging source
 MND
 http://library.link/vocab/creatorName
 Pohlers, Wolfram
 Dewey number
 511.36
 Image bit depth
 0
 Index
 index present
 Language note
 English
 LC call number
 QA9.54
 LC item number
 .P645 2009
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 Series statement
 Universitext
 http://library.link/vocab/subjectName

 Proof theory
 Logic, Symbolic and mathematical
 Logic, Symbolic and mathematical
 Beweistheorie
 Label
 Proof theory : the first step into impredicativity, Wolfram Pohlers
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references (pages 357361) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1 Historical Background  2 Primitive Recursive Functions and Relations  3 Ordinals  4 Pure Logic  5 Truth Complexities for Pi 11Sentences  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 NonMonotone Inductive Definitions  14 Epilogue
 Control code
 311303031
 Dimensions
 unknown
 Extent
 1 online resource (xiii, 370 pages).
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9783540693192
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783540693192
 http://library.link/vocab/ext/overdrive/overdriveId
 9783540693185
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)311303031
 Label
 Proof theory : the first step into impredicativity, Wolfram Pohlers
 Antecedent source
 mixed
 Bibliography note
 Includes bibliographical references (pages 357361) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 not applicable
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents
 1 Historical Background  2 Primitive Recursive Functions and Relations  3 Ordinals  4 Pure Logic  5 Truth Complexities for Pi 11Sentences  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 NonMonotone Inductive Definitions  14 Epilogue
 Control code
 311303031
 Dimensions
 unknown
 Extent
 1 online resource (xiii, 370 pages).
 File format
 multiple file formats
 Form of item
 online
 Isbn
 9783540693192
 Level of compression
 uncompressed
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Other control number
 10.1007/9783540693192
 http://library.link/vocab/ext/overdrive/overdriveId
 9783540693185
 Quality assurance targets
 absent
 Reformatting quality
 access
 Specific material designation
 remote
 System control number
 (OCoLC)311303031
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