Johnstone P.T. Notes on logic and set theory

Cambridge University Press, 1987. — 122 p.— (Cambridge Mathematical Textbooks) — ISBN: 0521-335027.This book has its origins in a course of lectures entitled 'Set Theory and Logic' which is given to third-year undergraduates in Cambridge. The Cambridge Mathematical Tripos contains rather little on the foundational aspects of mathematics: this course is (at the time of writing - though there are plans for a change before long) the only opportunity which undergraduates have to learn about the basic ideas of logic and axiomatic set theory in an examinable context, and its aim is therefore to provide a general introduction to these ideas for students who, though they may possess considerable sophistication in other areas of mathematics, have no previous experience of logic beyond a nodding acquaintance with 'naive' set theory, and whose primary interests may well lie in other areas of pure (or even applied) mathematics. Having lectured this course in 1984, 1985 and 1986,1 have been struck by the fact that there was no single textbook available covering both logic and set theory at the level of rigour and sophistication appropriate to such a course, and - in the belief that there might be universities other than Cambridge where the need for such a textbook was felt - I conceived the idea of expanding my lecture notes into a publishable text. I am glad to say that this idea was enthusiastically received by Cambridge University Press; I am grateful, in particular, to David Tranah and Martin Gilchrist for their support of the project.-Universal algebra
-Propositional calculus
-First-order theories
-Recursive functions
-Zermelo-Fraenkel set theory
-Ordinals and well-orderings
-The axiom of choice
-Cardinal arithmetic
-Consistency and independence