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.

Proof Theory

2013-01-01 Mathematics
Download Proof Theory PDF Online Free

Author :
Release : 2013-01-01
Genre : Mathematics
Kind : eBook
Book Rating : 734/5 ( reviews)

GET EBOOK


Book Synopsis Proof Theory by : Gaisi Takeuti

Download or read book Proof Theory written by Gaisi Takeuti. This book was released on 2013-01-01. Available in PDF, EPUB and Kindle. Book excerpt: 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

2012-12-06 Mathematics
Download Proof Theory PDF Online Free

Author :
Release : 2012-12-06
Genre : Mathematics
Kind : eBook
Book Rating : 733/5 ( reviews)

GET EBOOK


Book Synopsis Proof Theory by : K. Schütte

Download or read book Proof Theory written by K. Schütte. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: This book was originally intended to be the second edition of the book "Beweis theorie" (Grundlehren der mathematischen Wissenschaften, Band 103, Springer 1960), but in fact has been completely rewritten. As well as classical predicate logic we also treat intuitionistic predicate logic. The sentential calculus properties of classical formal and semiformal systems are treated using positive and negative parts of formulas as in the book "Beweistheorie". In a similar way we use right and left parts of formulas for intuitionistic predicate logic. We introduce the theory of functionals of finite types in order to present the Gi:idel interpretation of pure number theory. Instead of ramified type theory, type-free logic and the associated formalization of parts of analysis which we treated in the book "Beweistheorie", we have developed simple classical type theory and predicative analysis in a systematic way. Finally we have given consistency proofs for systems of lI~-analysis following the work of G. Takeuti. In order to do this we have introduced a constni'ctive system of notation for ordinals which goes far beyond the notation system in "Beweistheorie."

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.

Applied Proof Theory: Proof Interpretations and their Use in Mathematics

2008-05-23 Mathematics
Download Applied Proof Theory: Proof Interpretations and their Use in Mathematics PDF Online Free

Author :
Release : 2008-05-23
Genre : Mathematics
Kind : eBook
Book Rating : 331/5 ( reviews)

GET EBOOK


Book Synopsis Applied Proof Theory: Proof Interpretations and their Use in Mathematics by : Ulrich Kohlenbach

Download or read book Applied Proof Theory: Proof Interpretations and their Use in Mathematics written by Ulrich Kohlenbach. This book was released on 2008-05-23. Available in PDF, EPUB and Kindle. Book excerpt: 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.

You may also like...