Subsystems of Second Order Arithmetic

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Last edited by ImportBot
October 9, 2020 | History

Subsystems of Second Order Arithmetic

  • 1 Want to read

"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.

Publish Date
Language
English
Pages
444

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Previews available in: English

Edition Availability
Cover of: Subsystems of Second Order Arithmetic
Subsystems of Second Order Arithmetic
2010, Cambridge University Press
in English
Cover of: Subsystems of Second-Order Arithmetic
Subsystems of Second-Order Arithmetic
2010, Cambridge University Press
in English
Cover of: Subsystems of Second Order Arithmetic
Subsystems of Second Order Arithmetic
2009, Cambridge University Press
in English
Cover of: Subsystems of Second Order Arithmetic
Subsystems of Second Order Arithmetic
2009, Cambridge University Press
in English
Cover of: Subsystems of Second Order Arithmetic
Subsystems of Second Order Arithmetic
2009, Cambridge University Press
in English
Cover of: Subsystems of Second Order Arithmetic
Subsystems of Second Order Arithmetic
1999, Springer Berlin Heidelberg
electronic resource / in English
Cover of: Subsystems of Second Order Arithmetic
Subsystems of Second Order Arithmetic
Nov 05, 1998, Springer My Copy UK
paperback

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Book Details


Table of Contents

Preface
Acknowledgements
Table of Contents
Introduction
Part A. Development of Mathematics Within Subsystems
Recursive Comprehension
Arithmetical Comprehension.-Weak König's Lemma
Arithmetical Transfinite Recursion
Comprehension
Part B. Models of Subsystems of Z2
Beta-Models
Omega-Models
Non-Omega-Models
Appendix
Additional Results
Bibliography
Index
List of Tables. (For detailed Contents, see Contents Internet).

Edition Notes

Online full text is restricted to subscribers.

Also available in print.

Mode of access: World Wide Web.

Published in
Berlin, Heidelberg
Series
Perspectives in Mathematical Logic, Perspectives in mathematical logic

Classifications

Dewey Decimal Class
511.3
Library of Congress
QA8.9-10.3

The Physical Object

Format
[electronic resource] /
Pagination
1 online resource (xiv, 444p.)
Number of pages
444

ID Numbers

Open Library
OL27090051M
Internet Archive
subsystemssecond00simp_185
ISBN 10
3642642039, 3642599710
ISBN 13
9783642642036, 9783642599712
OCLC/WorldCat
851779348

Source records

Internet Archive item record

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October 9, 2020 Edited by ImportBot import existing book
July 7, 2019 Created by MARC Bot import new book