Lectures in Logic and Set Theory: Volume 1, Mathematical Logic (Cambridge Studies in Advanced Mathematics) 1st Edition
by
George Tourlakis
(Author)


ISBN-13: 978-0521168465
ISBN-10: 0521168465
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This two-volume work bridges the gap between introductory expositions of logic (or set theory) and the research literature. It can be used as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy. The volumes are written in a user-friendly lecture style that makes them equally effective for self-study or class use. Volume I includes formal proof techniques, applications of compactness (including nonstandard analysis), computability and its relation to the completeness phenonmenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen.
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Editorial Reviews
Review
"A thorough and complete resource for "one of the most remarkable theorems of logic." George Tourlakis' Mathematical Logic is a highly worthwhile addition the the literature."
Robert Mignone, The Review of Modern Logic
Robert Mignone, The Review of Modern Logic
Book Description
Meant as a text in an advanced undergraduate or beginning graduate course in mathematics, computer science, or philosophy, this two-volume work is written in a user-friendly conversational lecture style that makes it equally effective for self-study or class use.Volume II, on formal (ZFC) set theory, incorporates a self-contained "chapter 0" on proof techniques based on formal logic, in the style of Bourbaki. This provides the reader with a solid foundation in set theory, while the inclusion of topics such as absoluteness, relative consistency results, two expositions of Godel's constructible universe, numerous ways of viewing recursion, and a chapter on Cohen forcing, will usher the advanced reader to the doorstep of the research literature.
Product details
- Publisher : Cambridge University Press; 1st edition (September 1, 2010)
- Language : English
- Paperback : 342 pages
- ISBN-10 : 0521168465
- ISBN-13 : 978-0521168465
- Item Weight : 1.1 pounds
- Dimensions : 6 x 0.8 x 9 inches
- Best Sellers Rank: #3,787,530 in Books (See Top 100 in Books)
- #398 in Mathematical Set Theory
- #708 in Combinatorics (Books)
- #2,124 in Mathematical Logic
- Customer Reviews:
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Reviewed in the United States on September 26, 2013
This books provides an informal conversational introduction to mathematical logic. However, it does not sacrifice any rigor for it. In fact, every proof is as detailed as possible, making only arguments based on what has been previously proved and assumed. The author also lists exactly which of the previous arguments he used in proving some novel result. There are also frequent remarks and pauses to address questions that the reader might be asking in the middle of proofs. Of course, it is impossible to address every such question that might occur to every reader but, at least, the author tries (and mostly succeeds) to do so...something I find lacking in the vast majority of mathematical books out there on logic.
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Reviewed in the United States on August 23, 2015
Incredible achievement! A gem of a book. A very clear and detailed account of quite advanced and equally beautiful topics in Mathematical Logic including a complete proof of Godel's Second Theorem. I heartily recommend it. No specific prerequisites except that vague and nebulous "mathematical maturity"!