A Course in Mathematical Logic

John Lane Bell (born March 25, 1945) is Professor of Philosophy at the University of Western Ontario in Canada. He has made contributions to mathematical logic and philosophy, and is the author of a number of books. His research includes such topics as set theory, model theory, lattice theory, modal logic, quantum logic, constructive mathematics, type theory, topos theory, infinitesimal analysis, spacetime theory, and the philosophy of mathematics. He is the author of more than 70 articles and of 11 books. In 2009, he was elected a Fellow of the Royal Society of Canada. He was awarded a scholarship to Oxford University at the age of 15, and graduated with a D.Phil. in Mathematics: his dissertation supervisor was John Crossley. During 1968-89 he was Lecturer in Mathematics and Reader in Mathematical Logic at the London School of Economics.[1] John Bell's students include Graham Priest (Ph.D. Mathematics LSE, 1972), Michael Hallett (Ph.D. Philosophy LSE, 1979), Elaine Landry (Ph.D. Philosophy UWO, 1997), David DeVidi (Ph.D. Philosophy UWO, 1994) and Richard Feist (Ph.D. Philosophy UWO, 1999). BOOKS Intuitionistic Set Theory. College Publications, 2013. Set Theory: Boolean-Valued Models and Independence Proofs. Oxford University Press 2011. The Axiom of Choice. College Publications, 2009. The Continuous and the Infinitesimal in Mathematics and Philosophy. Polimetrica, 2005. (With D. DeVidi and G. Solomon) Logical Options: An Introduction to Classical and Alternative Logics. Broadview Press, 2001. The Art of the Intelligible: An Elementary Survey of Mathematics in its Conceptual Development. Kluwer, 1999. A Primer of Infinitesimal Analysis. Cambridge University Press, 1998. Second Edition, 2008. Toposes & Local Set Theories: An Introduction. Clarendon Press, Oxford, 1988. Reprinted by Dover, 2008. Boolean-Valued Models and Independence Proofs in Set Theory. Clarendon Press, Oxford, 1977. 2nd edition, 1985. 3rd edition, 2005. (With M. Machover). A Course in Mathematical Logic. North-Holland, Amsterdam, 1977. 4th printing, 2003. (With A. B. Slomson). Models and Ultraproducts: An Introduction. North-Holland, Amsterdam, 1969. Reprinted by Dover, 2006.

A comprehensive one-year graduate (or advanced undergraduate) course in mathematical logic and foundations of mathematics. No previous knowledge of logic is required; the book is suitable for self-study. Many exercises (with hints) are included. The book is valuable for anyone interested in mathematical logic and may serve as a reference source for graduate students and specialists.

1. Beginning Mathematical Logic. 2. First-Order Logic. 3. First-Order Logic (continued). 4. Boolean Algebras. 5. Model Theory. 6. Recursion Theory. 7. Logic - Limitative Results. 8. Recursion Theory (continued). 9. Intuitionistic First-Order Logic. 10. Axiomatic Set Theory. 11. Nonstandard Analysis. Bibliography.