Mathematical Logic

by Joseph R. Shoenfield

This classic introduction to the main areas of mathematical logic provides the basis for a first graduate course in the subject. It embodies the viewpoint that mathematical logic is not a collection of vaguely related results, but a coherent method of attacking some of the most interesting problems, which face the mathematician. The author presents the basic concepts in an unusually clear and accessible fashion, concentrating on what he views as the central topics of mathematical logic: proof theory, model theory, recursion theory, axiomatic number theory, and set theory. There are many exercises, and they provide the outline of what amounts to a second book that goes into all topics in more depth. This book has played a role in the education of many mature and accomplished researchers.

Genres: Mathematics, Logic

352 pages, Paperback

First published January 15, 2001

Reviews

[Stefko · Rating 4 out of 5]

This is one of the standard graduate-level texts in mathematical logic. It is amazing how the author covers such a wide variety of topic in less than 400 pages.

I find the chapter on set theory the most interesting. The book offers a good introduction to ZF. In about 100 pages it covers basics of set theory, constructable sets, forcing, independence of AC and GCH, large cardinals.