"Mathematical Logic" presents mathematical or "symbolic" logic as a reliable tool for deductive reasoning. It trains the student in both the established "Hilbert" style of writing proofs in mathematics, as well as in the emerging "equational" style that finds fruitful application in computer science curricula, especially in the areas of software engineering and program correctness. There are extensive sets of examples, remarks, problems, references, and textual discussions that aim to help the reader understand what makes logic a powerful tool in the scheme of mathematical truths.

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...

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).