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Lectures in Logic and Set Theory. Volume I: Mathematical Logic (Cambridge Studies in Advanced Mathematics) - George Tourlakis

Lectures in Logic and Set Theory. Volume I: Mathematical Logic (Cambridge Studies in Advanced Mathematics)

Author: George Tourlakis
Book title: Lectures in Logic and Set Theory. Volume I: Mathematical Logic (Cambridge Studies in Advanced Mathematics)
ISBN: 0521753732
ISBN13: 978-0521753739
Publisher: Cambridge University Press; 1st edition (January 13, 2003)
Language: English
Category: Mathematics
Rating: 4.7/5
Votes: 819
Pages: 342 pages
More formats: mobi mbr azw rtf

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.
Reviews: (2)
LiTTLe_NiGGa_in_THE_–°ribE
The book arrived in good condition. It was brand new as promised.

More than that though, the book's and in fact the series' subject-matter is amazing. It deals with how one can construct the basics of basics in mathematics, logic, from scratch using meta-theoretical, non-rigorous, naive set theory (in the 1st volume i.e. this book). Then it deals with how one can construct rigorous set theory out of this logic (in the 2nd volume of this book)! Fascinating how as one reads through this book and its sequel, one comes back ALMOST full circle to where one began (not an exact circle though since rigorous set theory is different from naive set theory; thus, there is technically no circular reasoning involved).

The author of this book is also very competent. He realizes that the subject of this book is pretty loaded. Hence he tries to foster as much understanding as possible with copious amounts of remarks, pauses and very detailed proofs. His style of explanation is also quite conversational rather than terse and abstruse. Hence, despite the book being meant for advanced math undergrads, it is actually accessible to pretty much any undergrad in math. All one needs is, as always, a love for mathematics. That being said, it would still be helpful to have SOME knowledge of, at least, naive set theory before one began. This is easily accomplish-able by either simply surfing the web on the subject-matter or waiting till one has taken an introductory real analysis course (actually any proof-oriented math course will do).
Mayno
My opinion is that this is the most readable and user friendly advanced book on Set Theory today. Especially the treatment of (Cohen's) Forcing is valuable, since other expositions on this subject were not suitable for beginning graduate students (Kunnen - very good, but very sophisticated, Jech - also good, but presents Forcing via Boolean Algebra, which is less widely used today, and the book is too long as an advance introduction).
Also the style or writing is inviting, and not intimidating.
Very significant book, pedagogically.
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