This is an introduction to logic and the axiomatization of set theory from a unique standpoint. Philosophical considerations, which are often ignored or treated casually, are here given careful consideration, and furthermore the author places the notion of inductively defined sets (recursive datatypes) at the centre of his exposition resulting in a treatment of well established topics that is fresh and insightful. The presentation is engaging, but always great care is taken to illustrate difficult points. Understanding is also aided by the inclusion of many exercises. Little previous knowledge of logic is required of the reader, and only a background of standard undergraduate mathematics is assumed.
- Inductively defined sets play a central role
- Great care is taken to motivate the axioms of set theory
- Philosophical concerns emphasised
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Reviews & endorsements
'This is a remarkable book, presenting an introduction to mathematical logic and axiomatic set theory from a unified standpoint … also eminently suitable for self-study by mature mathematicians who wish to acquire a well-balanced and deeper knowledge of a field that is not part of their specialty … The author's presentation is a model of clarity, and much of the liveliness of a lecture has been preserved in the write-up. The various asides, cross-references, and care in motivating definitions and concepts all contribute to the value of the book as an instructional source … a treasure in its genre, to be highly recommended by the reviewer.' MathSciNet
'… a real sense of freshness and vitality … I found this a very readable and stimulating book. Forster writes with an agreeably light touch and a whimsical sense of fun and his use of rectypes as a leitmotiv is both innovative and inspired.' The Mathematical Gazette
'The author's philosophical training leads him to accompany many definitions with lengthy reflexions which add interest and enliven the book.' Mathematika
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Product details
- Date Published: September 2003
- format: Hardback
- isbn: 9780521826211
- length: 244 pages
- dimensions: 238 x 158 x 20 mm
- weight: 0.449kg
- contains: 125 exercises
- availability: Available
Table of Contents
1. Definitions and notations
2. Recursive datatypes
3. Partially ordered sets
4. Propositional calculus
5. Predicate calculus
6. Computable functions
7. Ordinals
8. Set theory
9. Answers to selected questions.
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Instructors have used or reviewed this title for the following courses
- Introduction to Proof
- Mathematical Logic ll
Author
Thomas Forster, University of Cambridge

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Logic, Induction and Sets

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