Subsystems of Second Order Arithmetic / Edition 2

Subsystems of Second Order Arithmetic / Edition 2

by Stephen G. Simpson
     
 

ISBN-10: 052188439X

ISBN-13: 9780521884396

Pub. Date: 06/30/2009

Publisher: Cambridge University Press

Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics, with an eye to the unity of human knowledge. 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

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Overview

Foundations of mathematics is the study of the most basic concepts and logical structure of mathematics, with an eye to the unity of human knowledge. 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. Additional results are presented in an appendix.

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Product Details

ISBN-13:
9780521884396
Publisher:
Cambridge University Press
Publication date:
06/30/2009
Series:
Perspectives in Logic Series
Edition description:
Older Edition
Pages:
464
Product dimensions:
6.50(w) x 9.30(h) x 1.20(d)

Table of Contents

Preface
Acknowledgements
IIntroduction1
Pt. ADevelopment of Mathematics Within Subsystems of Z[subscript 2]
IIRecursive Comprehension63
IIIArithmetical Comprehension105
IVWeak Konig's Lemma127
VArithmetical Transfinite Recursion167
VI[Pi][subscript 1][superscript 1] Comprehension217
Pt. BModels of Subsystems of Z[subscript 2]
VII[beta]-Models245
VIII[omega]-Models313
IXNon-[omega]-Models363
XAdditional Results395
Bibliography413
Index425
List of Tables445

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