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 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 $/Pi_2$ 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)
- 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 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
- 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 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 $/Pi_2$ 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)
- 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 357-361) 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 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
- 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
- 10.1007/978-3-540-69319-2
- http://library.link/vocab/ext/overdrive/overdriveId
- 978-3-540-69318-5
- 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 357-361) 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 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
- 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
- 10.1007/978-3-540-69319-2
- http://library.link/vocab/ext/overdrive/overdriveId
- 978-3-540-69318-5
- Quality assurance targets
- absent
- Reformatting quality
- access
- Specific material designation
- remote
- System control number
- (OCoLC)311303031
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<div class="citation" vocab="http://schema.org/"><i class="fa fa-external-link-square fa-fw"></i> Data from <span resource="http://link.library.missouri.edu/portal/Proof-theory--the-first-step-into/Lam6w5Ebp9E/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.library.missouri.edu/portal/Proof-theory--the-first-step-into/Lam6w5Ebp9E/">Proof theory : the first step into impredicativity, Wolfram Pohlers</a></span> - <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.library.missouri.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.library.missouri.edu/">University of Missouri Libraries</a></span></span></span></span></div>