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

by H.-D. Ebbinghaus (Author),‎ J. Flum (Author),‎ Wolfgang Thomas (Author)

15 customer reviews

ISBN-13: 978-0387942582

ISBN-10: 0387942580

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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 Fraïssé's characterization of elementary equivalence, Lindström's theorem on the maximality of first-order logic, and the fundamentals of logic programming.

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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: 15 customer reviews
Amazon Best Sellers Rank: #1,495,750 in Books (See Top 100 in Books)
- #728 in Books > Science & Math > Mathematics > Pure Mathematics > Logic
- #2798 in Books > Education & Teaching > Schools & Teaching > Instruction Methods > Mathematics
- #12895 in Books > Textbooks > Science & Mathematics > Mathematics

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Charles Jacobsen

Excellent text for a step beyond intro level logic

December 29, 2015

Format: HardcoverVerified Purchase

Excellent text for senior undergraduates and beyond (this is not an introduction to logic). You should already be comfortable with rigorous mathematical proofs, including induction. Yes, there is a lot of notation, but it is consistently used and well-motivated. If you do research in this area, you will find that heaps of notation is typical. This will provide a great basis if you plan to do research in logic programming, SAT solvers, machine-checked proofs (via HOL, Coq, etc.), static analysis/formal verification, and so on. With this text, I clearly saw for the first time the difference between semantic and syntactic proofs and what it means for a system to be consistent or complete.

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Still good stuff.

January 15, 2018

Format: HardcoverVerified Purchase

Used this to teach undergraduate logic this past Fall semester. Still good stuff.

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Emre Domanic

Very good *mathematical* logic book

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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Pedro Zambrano

Four Stars

December 7, 2016

Format: HardcoverVerified Purchase

I got this book as promised.

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changli weng

Depressed!

March 16, 2012

Format: HardcoverVerified Purchase

This is the worst ML textbook I have ever read!
Not so bad in the contents but unfamiliar symbols and style
would confuse you.
Mendelson and Shoenfield's books are better options instead of this one!

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Nathan Oakes

Should be the standard undergrad introduction

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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Selmer Bringsjord

Excellent Choice for Teaching Mathematical Logic

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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Joshua Sklar

Excellent sourcebook for proofs and theorems; Not so great to learn from

June 10, 2013

Format: HardcoverVerified 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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Most recent customer reviews

Sankha S Basu

Will not suggest to anyone.

Not a very good text for beginners. There are other good books like the ones by Mendelson, A. Margaris and tons of others.

Published on December 17, 2008

Randall Helzerman

The steepest on-ramp to the fast lane of logic

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.Read more

Published on October 16, 2005

V. Alexander

Lots of typesets, and for what purpose?

I do not recommend it as an introduction to mathematical logic.
I found the material to be insufficiently motivated.Read more

Published on April 7, 2003

Todd Ebert

An excellent book, but not for beginners.

This is probably one of the best introductions to mathematical logic for those with sufficient mathematical maturity.Read more

Published on November 8, 2000

A customer

I hated this book.

This is perhaps the most cryptic book I have laid hands upon. The book can be written in a much simpler tone and as such, tends to confuse the reader more than it educates.Read more

Published on February 1, 1999

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