Proofs Theories
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Proof Theory
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Author : Gaisi Takeuti
language : en
Publisher: Courier Corporation
Release Date : 2013-01-01
Proof Theory written by Gaisi Takeuti and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-01 with Mathematics categories.
Focusing on Gentzen-type proof theory, this volume presents a detailed overview of creative works by author Gaisi Takeuti and other twentieth-century logicians. The text explores applications of proof theory to logic as well as other areas of mathematics. Suitable for advanced undergraduates and graduate students of mathematics, this long-out-of-print monograph forms a cornerstone for any library in mathematical logic and related topics. The three-part treatment begins with an exploration of first order systems, including a treatment of predicate calculus involving Gentzen's cut-elimination theorem and the theory of natural numbers in terms of Gödel's incompleteness theorem and Gentzen's consistency proof. The second part, which considers second order and finite order systems, covers simple type theory and infinitary logic. The final chapters address consistency problems with an examination of consistency proofs and their applications.
Proof Theory
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Author : Wolfram Pohlers
language : en
Publisher: Springer
Release Date : 2009-06-10
Proof Theory written by Wolfram Pohlers and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-06-10 with Mathematics categories.
Although this is an introductory text on proof theory, most of its contents is not found in a unified form elsewhere in the literature, except at a very advanced level. The heart of the book is the ordinal analysis of axiom systems, with particular emphasis on that of the impredicative theory of elementary inductive definitions on the natural numbers. The "constructive" consequences of ordinal analysis are sketched out in the epilogue. The book provides a self-contained treatment assuming no prior knowledge of proof theory and almost none of logic. The author has, moreover, endeavoured not to use the "cabal language" of proof theory, but only a language familiar to most readers.
An Introduction To Proof Theory
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Author : Paolo Mancosu
language : en
Publisher: Oxford University Press
Release Date : 2021-08-12
An Introduction To Proof Theory written by Paolo Mancosu and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-12 with Philosophy categories.
An Introduction to Proof Theory provides an accessible introduction to the theory of proofs, with details of proofs worked out and examples and exercises to aid the reader's understanding. It also serves as a companion to reading the original pathbreaking articles by Gerhard Gentzen. The first half covers topics in structural proof theory, including the Gödel-Gentzen translation of classical into intuitionistic logic (and arithmetic), natural deduction and the normalization theorems (for both NJ and NK), the sequent calculus, including cut-elimination and mid-sequent theorems, and various applications of these results. The second half examines ordinal proof theory, specifically Gentzen's consistency proof for first-order Peano Arithmetic. The theory of ordinal notations and other elements of ordinal theory are developed from scratch, and no knowledge of set theory is presumed. The proof methods needed to establish proof-theoretic results, especially proof by induction, are introduced in stages throughout the text. Mancosu, Galvan, and Zach's introduction will provide a solid foundation for those looking to understand this central area of mathematical logic and the philosophy of mathematics.
Structural Proof Theory
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Author : Sara Negri
language : en
Publisher: Cambridge University Press
Release Date : 2008-07-10
Structural Proof Theory written by Sara Negri and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-07-10 with Mathematics categories.
A concise introduction to structural proof theory, a branch of logic studying the general structure of logical and mathematical proofs.
Proofs Theories
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Author : Louise Gluck
language : en
Publisher: HarperCollins
Release Date : 2022-01-04
Proofs Theories written by Louise Gluck and has been published by HarperCollins this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-01-04 with Literary Collections categories.
Winner of the Nobel Prize in Literature Proofs and Theories, winner of the PEN/Martha Albrand Award for First Non-Fiction, is an illuminating collection of essays by Louise Glück, one of this country's most brilliant poets. Like her poems, the prose of Glück, who won the Pulitzer Prize for poetry in 1993 for The Wild Iris, is compressed, fastidious, fierce, alert, and absolutely unconsoled. The force of her thought is evident everywhere in these essays, from her explorations of other poets' work to her skeptical contemplation of current literary critical notions such as "sincerity" and "courage." Here also are Glück's revealing reflections on her own education and life as a poet, and a tribute to her teacher and mentor, Stanley Kunitz. Proofs and Theories is not a casual collection. It is the testament of a major poet.
Proof Theory
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Author : Peter Aczel
language : en
Publisher: Cambridge University Press
Release Date : 1992
Proof Theory written by Peter Aczel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Computers categories.
The lecture courses in this work are derived from the SERC 'Logic for IT' Summer School and Conference on Proof Theory held at Leeds University. The contributions come from acknowledged experts and comprise expository and research articles; put together in this book they form an invaluable introduction to proof theory that is aimed at both mathematicians and computer scientists.
Mathematical Intuitionism
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Author : Al'bert Grigor'evi_ Dragalin
language : en
Publisher: American Mathematical Soc.
Release Date : 1988-12-31
Mathematical Intuitionism written by Al'bert Grigor'evi_ Dragalin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-12-31 with Mathematics categories.
In the area of mathematical logic, a great deal of attention is now being devoted to the study of nonclassical logics. This book intends to present the most important methods of proof theory in intuitionistic logic and to acquaint the reader with the principal axiomatic theories based on intuitionistic logic.
Applied Proof Theory Proof Interpretations And Their Use In Mathematics
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Author : Ulrich Kohlenbach
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-23
Applied Proof Theory Proof Interpretations And Their Use In Mathematics written by Ulrich Kohlenbach and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-23 with Mathematics categories.
This is the first treatment in book format of proof-theoretic transformations - known as proof interpretations - that focuses on applications to ordinary mathematics. It covers both the necessary logical machinery behind the proof interpretations that are used in recent applications as well as – via extended case studies – carrying out some of these applications in full detail. This subject has historical roots in the 1950s. This book for the first time tells the whole story.
Proof Theory
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Author : Wolfram Pohlers
language : en
Publisher:
Release Date : 2014-01-15
Proof Theory written by Wolfram Pohlers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Ways Of Proof Theory
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Author : Ralf Schindler
language : en
Publisher: Walter de Gruyter
Release Date : 2013-05-02
Ways Of Proof Theory written by Ralf Schindler and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-05-02 with Philosophy categories.
On the occasion of the retirement of Wolfram Pohlers the Institut für Mathematische Logik und Grundlagenforschung of the University of Münster organized a colloquium and a workshop which took place July 17 – 19, 2008. This event brought together proof theorists from many parts of the world who have been acting as teachers, students and collaborators of Wolfram Pohlers and who have been shaping the field of proof theory over the years. The present volume collects papers by the speakers of the colloquium and workshop; and they produce a documentation of the state of the art of contemporary proof theory.