Share

An Introduction to Proof Theory

2021 Philosophy
Download An Introduction to Proof Theory PDF Online Free

Author :
Release : 2021
Genre : Philosophy
Kind : eBook
Book Rating : 931/5 ( reviews)

GET EBOOK


Book Synopsis An Introduction to Proof Theory by : Paolo Mancosu

Download or read book An Introduction to Proof Theory written by Paolo Mancosu. This book was released on 2021. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Ordinal Analysis with an Introduction to Proof Theory

2020-08-11 Philosophy
Download Ordinal Analysis with an Introduction to Proof Theory PDF Online Free

Author :
Release : 2020-08-11
Genre : Philosophy
Kind : eBook
Book Rating : 590/5 ( reviews)

GET EBOOK


Book Synopsis Ordinal Analysis with an Introduction to Proof Theory by : Toshiyasu Arai

Download or read book Ordinal Analysis with an Introduction to Proof Theory written by Toshiyasu Arai. This book was released on 2020-08-11. Available in PDF, EPUB and Kindle. Book excerpt: This book provides readers with a guide to both ordinal analysis, and to proof theory. It mainly focuses on ordinal analysis, a research topic in proof theory that is concerned with the ordinal theoretic content of formal theories. However, the book also addresses ordinal analysis and basic materials in proof theory of first-order or omega logic, presenting some new results and new proofs of known ones.Primarily intended for graduate students and researchers in mathematics, especially in mathematical logic, the book also includes numerous exercises and answers for selected exercises, designed to help readers grasp and apply the main results and techniques discussed.

An Introduction to Proof Theory

2021-08-12 Philosophy
Download An Introduction to Proof Theory PDF Online Free

Author :
Release : 2021-08-12
Genre : Philosophy
Kind : eBook
Book Rating : 299/5 ( reviews)

GET EBOOK


Book Synopsis An Introduction to Proof Theory by : Paolo Mancosu

Download or read book An Introduction to Proof Theory written by Paolo Mancosu. This book was released on 2021-08-12. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Proof Theory

2009-06-10 Mathematics
Download Proof Theory PDF Online Free

Author :
Release : 2009-06-10
Genre : Mathematics
Kind : eBook
Book Rating : 250/5 ( reviews)

GET EBOOK


Book Synopsis Proof Theory by : Wolfram Pohlers

Download or read book Proof Theory written by Wolfram Pohlers. This book was released on 2009-06-10. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Handbook of Proof Theory

1998-07-09 Mathematics
Download Handbook of Proof Theory PDF Online Free

Author :
Release : 1998-07-09
Genre : Mathematics
Kind : eBook
Book Rating : 183/5 ( reviews)

GET EBOOK


Book Synopsis Handbook of Proof Theory by : S.R. Buss

Download or read book Handbook of Proof Theory written by S.R. Buss. This book was released on 1998-07-09. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains articles covering a broad spectrum of proof theory, with an emphasis on its mathematical aspects. The articles should not only be interesting to specialists of proof theory, but should also be accessible to a diverse audience, including logicians, mathematicians, computer scientists and philosophers. Many of the central topics of proof theory have been included in a self-contained expository of articles, covered in great detail and depth. The chapters are arranged so that the two introductory articles come first; these are then followed by articles from core classical areas of proof theory; the handbook concludes with articles that deal with topics closely related to computer science.

You may also like...