Logic, Induction and Sets

This is an introduction to logic and the axiomatization of set theory from a unique standpoint.

Thomas Forster (Author)

9780521533614, Cambridge University Press

Paperback, published 21 July 2003

246 pages, 125 exercises
22.9 x 15.2 x 1.3 cm, 0.34 kg

'The author's philosophical training leads him to accompany many definitions with lengthy reflexions which add interest and enliven the book.' Mathematika

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.

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.

Subject Areas: Set theory [PBCH], Mathematical logic [PBCD], Philosophy of mathematics [PBB]