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This introduction to first-order logic clearly works out the role of first-order logic in the foundations of mathematics, particularly the two basic questions of the range of the axiomatic method and of theorem-proving by machines. It covers several advanced topics not commonly treated in introductory texts, such as Fra�ss�'s characterization of elementary equivalence, Lindstr�m's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
- Sales Rank: #899435 in Books
- Published on: 1996-11-15
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x .81" w x 6.14" l, 1.30 pounds
- Binding: Hardcover
- 291 pages
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
From the Back Cover
The book starts with a thorough treatment of first-order logic and its role in the foundations of mathematics. It covers several advanced topics, not commonly treated in introductory texts, such as Trachtenbrot's undecidability theorem Fraisse's characterization of elementary equivalence, Lindstrom's theorem on the maximality of first-order logic, and the fundamentals of logic programming.
Most helpful customer reviews
23 of 24 people found the following review helpful.
Very good *mathematical* logic book
By Emre Domanic
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.
17 of 21 people found the following review helpful.
The steepest on-ramp to the fast lane of logic
By Randall Helzerman
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 :-)
5 of 5 people found the following review helpful.
Excellent Choice for Teaching Mathematical Logic
By Selmer Bringsjord
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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