An Algebraic Introduction to Mathematical Logic / by D.W. Barnes, J.M. Mack.

Format:

Book

Author/Creator:

Barnes, D. W. (Donald W.), 1935- author.

Mack, J. M., author.

Contributor:

SpringerLink (Online service)

Series:

Graduate texts in mathematics 2197-5612 ; 22.

Graduate Texts in Mathematics, 2197-5612 ; 22

Language:

English

Subjects (All):

Logic, Symbolic and mathematical.

Algebra.

Mathematical Logic and Foundations.

Local Subjects:

Mathematical Logic and Foundations.

Algebra.

Physical Description:

1 online resource (IX, 123 pages).

Edition:

First edition 1975.

Contained In:

Springer Nature eBook

Place of Publication:

New York, NY : Springer New York : Imprint: Springer, 1975.

System Details:

text file PDF

Summary:

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 of the sub-ject 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, et cetera 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.

Contents:

I Universal Algebra

II Propositional Calculus

III Properties of the Propositional Calculus

IV Predicate Calculus

V First-Order Mathematics

VI Zermelo-Fraenkel Set Theory

VII Ultraproducts

VIII Non-Standard Models

IX Turing Machines and Gödel Numbers

X Hilbert's Tenth Problem, Word Problems

References and Further Reading

Index of Notations.

Other Format:

Printed edition:

ISBN:

9781475744897

Access Restriction:

Restricted for use by site license.