Lectures in Logic and Set Theory, Volume 2: Set Theory (Cambridge Studies in Advanced Mathematics)

Volume II, on formal (ZFC) set theory, incorporates a self-contained "chapter 0" on proof techniques so that it is based on formal logic, in the style of Bourbaki. The emphasis on basic techniques provides a solid foundation in set theory and a thorough context for the presentation of advanced topics (such as absoluteness, relative consistency results, two expositions of Godel's construstive universe, numerous ways of viewing recursion and Cohen forcing).

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 I includes formal proof techniques, a section on applications of compactness (including nonstandard analysis), a generous dose of computability and its relation to the incompleteness phenomenon, and the first presentation of a complete proof of Godel's 2nd incompleteness since Hilbert and Bernay's Grundlagen.