# An Algebraic Introduction to Mathematical Logic

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

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

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 sub stantial course on abstract algebra. Consequently, our treatment ofthe sub ject is algebraic. Although we assurne 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 assurne 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 oflogic 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 co me only by analogy with the model, and are to be regarded in much the same way as the conclusions drawn from any scientific theory.

algebra mathematical logic set theory

- DOI https://doi.org/10.1007/978-1-4757-4489-7
- Copyright Information Springer-Verlag New York 1975
- Publisher Name Springer, New York, NY
- eBook Packages Springer Book Archive
- Print ISBN 978-1-4757-4491-0
- Online ISBN 978-1-4757-4489-7
- Series Print ISSN 0072-5285
- About this book