An Algebraic Introduction To Mathematical Logic
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An Algebraic Introduction to Mathematical Logic
Author: D.W. Barnes
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-06-29
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.
Algebraic Logic
Author: Semen Grigorʹevich Gindikin
language: en
Publisher: Springer Science & Business Media
Release Date: 1985-10-14
The popular literature on mathematical logic is rather extensive and written for the most varied categories of readers. College students or adults who read it in their free time may find here a vast number of thought-provoking logical problems. The reader who wishes to enrich his mathematical background in the hope that this will help him in his everyday life can discover detailed descriptions of practical (and quite often -- not so practical!) applications of logic. The large number of popular books on logic has given rise to the hope that by applying mathematical logic, students will finally learn how to distinguish between necessary and sufficient conditions and other points of logic in the college course in mathematics. But the habit of teachers of mathematical analysis, for example, to stick to problems dealing with sequences without limit, uniformly continuous functions, etc. has, unfortunately, led to the writing of textbooks that present prescriptions for the mechanical construction of definitions of negative concepts which seem to obviate the need for any thinking on the reader's part. We are most certainly not able to enumerate everything the reader may draw out of existing books on mathematical logic, however.
An Algebraic Introduction to Mathematical Logic
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.