Proof theory : the first step into impredicativity
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The work Proof theory : the first step into impredicativity represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
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Proof theory : the first step into impredicativity
Resource Information
The work Proof theory : the first step into impredicativity represents a distinct intellectual or artistic creation found in University of Missouri Libraries. This resource is a combination of several types including: Work, Language Material, Books.
 Label
 Proof theory : the first step into impredicativity
 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
 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
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