This short textbook provides a succinct introduction to
mathematical logic and set theory, which together form the
foundations for the rigorous development of mathematics. It will be
suitable for all mathematics undergraduates coming to the subject
for the first time. The book is based on lectures given at the
University of Cambridge and covers the basic concepts of logic:
first order logic, consistency, and the completeness theorem,
before introducing the reader to the fundamentals of axiomatic set
theory. There are also chapters on recursive functions, the axiom
of choice, ordinal and cardinal arithmetic and the incompleteness
theorems. Dr Johnstone has included numerous exercises designed to
illustrate the key elements of the theory and to provide
applications of basic logical concepts to other areas of
mathematics. Consequently the book, while making an attractive
first textbook for those who plan to specialise in logic, will be
particularly valuable for mathematics and computer scientists whose
primary interests lie elsewhere.
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