Introduction To The Theory Of Logic
By addebook • Oct 13th, 2008 • Category: Mathematics
Introduction To The Theory Of Logic
Introduction To The Theory Of Logic
By Jose L. Zalabardo
Publisher: Westview Press
Number Of Pages: 344
Publication Date: 2000-01-11
ISBN-10 / ASIN: 081336602X
ISBN-13 / EAN: 9780813366029
Binding: Paperback
This book provides a rigorous introduction to the basic concepts and results of contemporary logic. It also presents, in two unhurried chapters, the mathematical tools (mainly from set theory) that are needed to master the technical aspects of the subject. Methods of definition and proof are also discussed at length, with special emphasis on inductive definitions and proofs and recursive definitions. The book is ideally suited for readers who want to undertake a serious study of logic but lack the mathematical background that other texts at this level presuppose. It can be used as a textbook in graduate and advanced undergraduate courses in logic. Hundreds of exercises are provided. Topics covered include basic set theory, propositional and first-order syntax and semantics, a sequent calculus-style deductive system, the soundness and completeness theorems, cardinality, the expressive limitations of first-order logic, with especial attention to the Loewenheim-Skolem theorems and non-standard models of arithmetic, decidability, complete theories, categoricity and quantifier elimination.
Summary: Logic with avengence!
Rating: 5
This is one heck of a tough book! It works from the ground up, starting with set theory, and gives you everything you ever wanted to know about metalogic. It’s also nice for reference if you suddenly blank out on such things as what a strict ordering is, etc.
My only complaint is that there aren’t solutions to even some of the exercises and a little too much “left as an exercise for the reader.”
Why authors of books like this call them “introductions” I can’t fathom. It’s rather like the mathematicians’ “it is easy to show…” Yeah. Right. One could, in theory, learn logic from the ground up by working through this book because it’s all there, but for practical purposes you really either have to have done a first logic course or have a decent level of mathematical maturity to cope with it.
But if you have that background, really want to nail it and go deeper and further, this is about the best book of its kind I’ve seen.
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