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Title: Mathematical Logic by H.-D. Ebbinghaus, J. Flum, W. Thomas ISBN: 0-387-94258-0 Publisher: Springer-Verlag Pub. Date: 01 June, 1994 Format: Hardcover Volumes: 1 List Price(USD): $59.95 |
Average Customer Rating: 3.86 (7 reviews)
Rating: 4
Summary: Restrained, Serious, Comprehensive: A Revolutionary Textbook
Comment: The best introduction to formal logic currently available, Ebbinghaus and Flum's *Mathematical Logic* drops the technique of "talking to cannibals" complained about by G.H. Hardy. Namely, Hardy couldn't do that anymore, and that was a long time ago: but for a long time readable logic texts (that is, texts not dedicated to the extrusion of logical categories from more copacetic algebraic ones) maintained a publicist's mien concerning the subject. Not so with this, but Ebbinghaus and Flum secretly maintain the publicist's attitude: this book covers more topics more thoroughly and elegantly than any of its competitors (including Wilfrid Hodges' much-touted, elsewhere-needed *A Shorter Model Theory*), including many topics of significance to graduate students in mathematics (infinitary logic, generalized quantifiers).
It really deserves to become the backbone of logic education -- that is, students deserve this and not half-hearted or whole-hog texts. For once, Springer is not blotting a superior product out of the market, but don't be confused: this is a rare occasion, as the serious aficionado of formal logic looks to North-Holland for guidance and Cambridge for avoidance. Not all "yellows" are equally mellow, and Springer's glut of nuvotexts is to be avoided like the intellectual plague it is -- many trends of the intellectual present cover up deeper perspectives with more appealing "localizations" not written all over them.
Rating: 2
Summary: Lots of typesets, and for what purpose?
Comment: I do not recommend it as an introduction to mathematical logic.
I found the material to be insufficiently motivated. Unfortunately, the authors take some of their variables from an old english alphabet, which ruins the aesthetics. I am sure that some elegant and glorious principles are expounded here. But it was not written clearly enough for me to see them.
Rating: 5
Summary: An excellent book, but not for beginners.
Comment: This is probably one of the best introductions to mathematical logic for those with sufficient mathematical maturity. I especially enjoyed the treatment of the completeness theorem for first-order logic (using Henkin's Theorem), and the treatment of Godel's incompleteness theorem, and Trachtenbrachts incompleteness theorem for second-order logic. Compared to other books, this book tends to go light on the notation.
If you do not have sufficient math maturity, then you may want to try Smullyan's book on the subject.
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Title: A Mathematical Introduction to Logic by Herbert B. Enderton ISBN: 0122384520 Publisher: Academic Press Pub. Date: December, 2000 List Price(USD): $83.95 |
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Title: Basic Proof Theory by A. S. Troelstra, H. Schwichtenberg, Anne S. Troelstra ISBN: 0521779111 Publisher: Cambridge University Press Pub. Date: 01 September, 2000 List Price(USD): $35.00 |
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Title: Set Theory by Thomas J. Jech ISBN: 3540440852 Publisher: Springer-Verlag Pub. Date: 19 November, 2002 List Price(USD): $139.00 |
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Title: Model Theory: An Introduction by D. Marker, David Marker ISBN: 0387987606 Publisher: Springer-Verlag Pub. Date: 21 August, 2002 List Price(USD): $59.95 |
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Title: Understanding the Infinite by Shaughan Lavine ISBN: 0674921178 Publisher: Harvard University Press Pub. Date: 01 March, 1998 List Price(USD): $22.95 |
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