Mathematical Logic [Paperback]

Joseph R. Shoenfield (Author)

Book Description

ISBN-10: 1568811357 | ISBN-13: 978-1568811352 | Publication Date: January 15, 2001 | Edition: 1st

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.

Editorial Reviews

Review

" ""classic text is as fresh and useful today as when first published. Noted for the economy of its presentation, it includes a wealth of basic and key results from all parts of mathematical logic."" -Solomon Feferman, Stanford University, January 2001
""The book remains an excellent introduction to logic . . . reads as a continuous whole, not a set of isolated topics . . . "" -C. W. Kilmister, The Mathematical Gazette, July 2003"

Product Details

• Paperback: 356 pages
• Publisher: A K Peters/CRC Press; 1st edition (January 15, 2001)
• Language: English
• ISBN-10: 1568811357
• ISBN-13: 978-1568811352
• Product Dimensions: 9.2 x 6.5 x 0.8 inches
• Shipping Weight: 1.2 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #602,541 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

28 of 31 people found the following review helpful:

3.0 out of 5 stars Standard by default, July 11, 2005

By 

Nathan Oakes (Ashland, Oregon) - See all my reviews

This review is from: Mathematical Logic (Paperback)

Almost four decades after being written, this is still the standard graduate survey text. A large part of the reason is that there is little competition, but it is also a good book on its own merits. The author writes with a clarity and concision you rarely see in a math (or any) textbook. Proofs are straighforward, not tricky or convoluted. There are many excercises and with detailed setup. The exercises are often quite hard, requiring significant extension from the text.

Although the writing is good, that doesn't mean it is easy. He progresses deliberately through the details, rarely giving an overview. I think he is just expecting that you already have a good sense of context from the undergrad logic course you took (didn't you?). Sometimes he seems to belabor a point. There is also a dearth of examples, just five in the whole book, three of them in the appendix. There are no references at all. The age of the book makes it, not wrong, but inadequate in some areas. Still, I have looked at alternatives and haven't found something better for a graduate survey text in English.

28 of 36 people found the following review helpful:

5.0 out of 5 stars Rock-solid introduction to Mathematical Logic, February 19, 2001

By 

Pedro L. Ribeiro "lqp-man" (Cotia, SP Brazil) - See all my reviews
(REAL NAME)   

This review is from: Mathematical Logic (Paperback)

Since my first contact with mathematical logic, I've always seen it as a kind of brainwashing, forcing one's mind to work based on several little pieces of thought. Nevertheless, it can be described as "a necessary evil", because the mindless use of mathematical logic throughout mathematics is very treacherous, as it can be seen in the problems regarding the axiom of choice, the Banach-Tarski paradox in measure theory, the issues about the undecidability of certain assumptions in set theory, and the very limitations of mathematical logic.

Usually, of course, most work in mathematics doesn't require a deep knowledge of rigorous mathematical logic, but it's always a good thing to a serious mathematician to have some acquaintance with it, even if it's just to avoid boobytraps. Then, it's hard to find a better choice than Shoenfield's book. After a long absence from the book market, A K Peters made the wise decision of reprint this masterpiece. Although most of its contents are fairly standard for a book on mathematical logic (unlike the equally marvellous out-of-print book of Yu. I. Manin, which has a more philosophical slant and concerns itself with issues such as quantum logic, literature, etc.), it provides proofs for many propositions that in most of the literature are only stated. It has, of course, some extras not generally found in other books, as for example issues concerning constructibility of sets.

But the most important characteristic of this book is its clarity and precision. It doesn't waste time in unnecessary stuff, and shows why we need mathamatical logic at all. Although it lacks some topics (for example, it doesn't discuss other axiomatic set theories besides Zermelo-Fraenkel. This is not so nice, because it lacks the distinction between classes and sets, one of the tenets of the Goedel- -Bernays-von Neumann set theory, although it is conceptually easier than this last one. But maybe it's a pedagogical choice, because the set theory we all intuitively know is more or less based in Zermelo-Fraenkel), its main concern is pedagogy, so this limitation has a sound reason: this book exposes mainly the logic present in the math most mathematicians and alike scientists (mathematical physicists, etc.) use. Its solidity and razor-sharp precision is great to instruct these people to be more careful with the math they use.

Besides that, some of the missing topics can be complemented by Mendelsson's "Introduction to Mathematical Logic", which is a bit more "merciful" book, which, by the other side, welcomes the thoroughness of Shoenfield.