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An Algebraic Introduction to Mathematical Logic
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Catalogue Information
Field name
Details
Dewey Class
511.3
Title
An Algebraic Introduction to Mathematical Logic ([EBook] /) / by Donald W. Barnes, John M. Mack.
Author
Barnes, Donald W.
Added Personal Name
Mack, John M.
author.
Other name(s)
SpringerLink (Online service)
Publication
New York, NY : : Springer New York : : Imprint: Springer, , 1975.
Physical Details
IX, 123 p. : online resource.
Series
Graduate texts in mathematics
0072-5285 ; ; 22
ISBN
9781475744897
Summary Note
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.:
Contents note
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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site
http://dx.doi.org/10.1007/978-1-4757-4489-7
Links to Related Works
Subject References:
Algebra
.
Mathematical logic
.
Mathematical Logic and Foundations
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Mathematics
.
Authors:
Barnes, Donald W.
.
Mack, John M.
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Corporate Authors:
SpringerLink (Online service)
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Series:
Graduate texts in mathematics
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GTM
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Classification:
511.3
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