HANDBOOK OF REVERSE MATHEMATICS

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Overview of Book :

This a book about the foundations of mathematics—a topic once of interest to outstanding mathematicians, such as Dedekind, Poincare, and Hilbert, but today sadly neglected. This neglect is unfortunate for several reasons: 

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• As mathematics splits into more and more specialties, the need for a uni fying viewpoint becomes more acute. 

• Foundations unify not only mathematics but also the neighboring disci plines of computer science and physics. 

• Recent advances in mathematical logic throw new light on the foundations of analysis, and on the elusive concept of mathematical “depth.” 

This book aims at the last point in particular, by focusing on the topic of reverse mathematics. 

Table of contents :

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1. Historical Introduction 

2. Classical Arithmetization 

3. Classical Analysis 

4. Computability 

5. Arithmetization of Computation 

6. Arithmetical Comprehension 

7. Recursive Comprehension 

8. A Bigger Picture 

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