Mathematical Logic, 2nd Edition (Undergraduate Texts in Mathematics) 2nd Edition by H.-D. Ebbinghaus (PDF)

Description

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.

User’s Reviews

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 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.

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐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.

⭐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.

⭐I got this book as promised.

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

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

⭐My fourth logic textbook. Great introduction. What does the picture on the cover mean?

⭐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.

⭐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 🙂

⭐Good book for a good price. Clear explanations and examples. Only possible downside is an overly minimalistic style for notation.

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