Subsystems of Second Order Arithmetic PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Subsystems of Second Order Arithmetic PDF full book. Access full book title Subsystems of Second Order Arithmetic by Stephen George Simpson. Download full books in PDF and EPUB format.
Author: Stephen G. Simpson Publisher: ISBN: 9783642599712 Category : Computer science Languages : en Pages : 444
Book Description
"From the point of view of the foundations of mathematics, this definitive work by Simpson is the most anxiously awaited monograph for over a decade. The "subsystems of second order arithmetic" provide the basic formal systems normally used in our current understanding of the logical structure of classical mathematics. Simpson provides an encyclopedic treatment of these systems with an emphasis on *Hilbert's program* (where infinitary mathematics is to be secured or reinterpreted by finitary mathematics), and the emerging *reverse mathematics* (where axioms necessary for providing theorems are determined by deriving axioms from theorems). The classical mathematical topics treated in these axiomatic terms are very diverse, and include standard topics in complete separable metric spaces and Banach spaces, countable groups, rings, fields, and vector spaces, ordinary differential equations, fixed points, infinite games, Ramsey theory, and many others. The material, with its many open problems and detailed references to the literature, is particularly valuable for proof theorists and recursion theorists. The book is both suitable for the beginning graduate student in mathematical logic, and encyclopedic for the expert." Harvey Friedman, Ohio State University.
Author: Stephen G. Simpson Publisher: Cambridge University Press ISBN: 1139478915 Category : Mathematics Languages : en Pages : 445
Book Description
Almost all of the problems studied in this book are motivated by an overriding foundational question: What are the appropriate axioms for mathematics? Through a series of case studies, these axioms are examined to prove particular theorems in core mathematical areas such as algebra, analysis, and topology, focusing on the language of second-order arithmetic, the weakest language rich enough to express and develop the bulk of mathematics. In many cases, if a mathematical theorem is proved from appropriately weak set existence axioms, then the axioms will be logically equivalent to the theorem. Furthermore, only a few specific set existence axioms arise repeatedly in this context, which in turn correspond to classical foundational programs. This is the theme of reverse mathematics, which dominates the first half of the book. The second part focuses on models of these and other subsystems of second-order arithmetic.
Author: Denis R Hirschfeldt Publisher: World Scientific ISBN: 9814612634 Category : Mathematics Languages : en Pages : 231
Book Description
This book is a brief and focused introduction to the reverse mathematics and computability theory of combinatorial principles, an area of research which has seen a particular surge of activity in the last few years. It provides an overview of some fundamental ideas and techniques, and enough context to make it possible for students with at least a basic knowledge of computability theory and proof theory to appreciate the exciting advances currently happening in the area, and perhaps make contributions of their own. It adopts a case-study approach, using the study of versions of Ramsey's Theorem (for colorings of tuples of natural numbers) and related principles as illustrations of various aspects of computability theoretic and reverse mathematical analysis. This book contains many exercises and open questions.
Author: Petr Hájek Publisher: Cambridge University Press ISBN: 1107168414 Category : Mathematics Languages : en Pages : 475
Book Description
A much-needed monograph on the metamathematics of first-order arithmetic, paying particular attention to fragments of Peano arithmetic.
Author: John Stillwell Publisher: Princeton University Press ISBN: 0691196419 Category : Mathematics Languages : en Pages : 198
Book Description
This volume presents reverse mathematics to a general mathematical audience for the first time. Stillwell gives a representative view of this field, emphasizing basic analysis--finding the "right axioms" to prove fundamental theorems--and giving a novel approach to logic. to logic.
Author: S.R. Buss Publisher: Elsevier ISBN: 0080533183 Category : Mathematics Languages : en Pages : 823
Book Description
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.
Author: Stephen George Simpson
Author: Stephen George Simpson
Author: Stephen G. Simpson
Author: Stephen G. Simpson
Author: Robert Alan Van Wesep
Author: Jeremy David Avigad
Author: Denis R Hirschfeldt
Author: Petr Hájek
Author: John Stillwell
Author: 
Author: S.R. Buss