Mathematical Logic, 2nd Edition (Undergraduate Texts in Mathematics) 2nd Edition

12 customer reviews
ISBN-13: 978-0387942582
ISBN-10: 0387942580
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Editorial Reviews

Review

"...the book remains my text of choice for this type of material, and I highly recommend it to anyone teaching a first logic course at this level." - Journal of Symbolic Logic

Language Notes

Text: English (translation)
Original Language: German
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Product Details

  • Series: Undergraduate Texts in Mathematics
  • Hardcover: 291 pages
  • Publisher: Springer; 2nd edition (November 15, 1996)
  • Language: English
  • ISBN-10: 0387942580
  • ISBN-13: 978-0387942582
  • Product Dimensions: 6.1 x 0.8 x 9.2 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 3.2 out of 5 stars  See all reviews (12 customer reviews)
  • Amazon Best Sellers Rank: #1,281,753 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

22 of 23 people found the following review helpful By Emre Domanic on December 9, 1999
Format: Hardcover
This is *the* excellent mathematical logic book for anyone sufficiently familiar with the aims and spirit of mathematical logic. However, it is probably *not* suitable for a first introduction.
Some of the informal discussion expects the reader to supply the sense, and hence could be misleading for a novice (or even incorrect if taken literally!) On the other hand, the discussion is crystal clear and illuminating for someone with a bit more of background.
This book will not provide philosophical enlightenment to students of logic (esp. to those who seek such enlightenment in the first place), but it will provide good understanding of the study of general mathematical structures and their relation to logic. The prospective reader should first get acquainted with the model theoretic point of view (i.e. with its aims and presuppositions) before tackling this book. Good sources are: the first few chapters of Wilfrid Hodges's "A Shorter Model Theory" and the relevant articles by Jaakko Hintikka which were published in the journal "Synthese" in the late 1980's.
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14 of 14 people found the following review helpful By Nathan Oakes on July 11, 2005
Format: Hardcover
Intended for a one-semester course, it ignores some of the usual topics in a survey course so it can give a deeper treatment of the nature and adequacy of mathematical proofs. It slights number theory, second-order logic, nonstandard analysis, and set theory. There is only enough on recursion and computability to support the main topic, but it goes deeper than usual on limitative results.

What it does cover it does very well. Motivation is rich and exercises follow well from the text. Proofs are very clear. Overall, there is much greater coherence in the development of ideas than you usually see in a survey text.

While the writing is very good, there is a shortage of definitions, examples, and exercises. Notation is not always clearly introduced and they adopt so many abbreviations it's hard to keep track of what things mean. I also thought that it was not as clear in the second half, maybe due to the multiple authors. Still, I would choose it over Enderton unless you need lots of exercises for class use.
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14 of 15 people found the following review helpful By Todd Ebert on November 8, 2000
Format: Hardcover
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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17 of 21 people found the following review helpful By Randall Helzerman on October 16, 2005
Format: Hardcover
Learning mathematical logic from this textbook is a little like learning to rock-climb by going straight to the half-dome. Most likely, you'll fall to your death. But if you're strong enough and lucky enough to endure the climb, you'll look back on how far you've come and have an "OH MY GOD I ACTUALLY DID THAT???" moment of clarity like nothing else you've ever experienced :-)
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5 of 5 people found the following review helpful By Selmer Bringsjord on March 20, 2007
Format: Digital
This is a truly excellent book -- one I've used (along with other other books) to teach mathematical logic for 20 years. (The new edition provided welcome coverage of logic programming.) Traditionally, logic pedagogy has tended to revolve around which colleges or universities are involved. You will need to have sharp students to take full advantage of this textbook. In addition, some proof construction environment/proof checker is a good thing to have accompany the textbook; the same would hold of model finders. For grad students in my lab, I require familiarity with the book, sooner or later.
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3 of 3 people found the following review helpful By Joshua Sklar on June 10, 2013
Format: Hardcover Verified Purchase
The title of this review really says it all. If you are already familiar with the theorems inside, this is probably an excellent way of brushing up on your metalogic. However, if you are a first time learner, the stuff is going to be frustratingly condensed at best and hopelessly opaque at worst.
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