Description: This textbook gives a complete and modern introduction to mathematical logic. The author uses contemporary notation, conventions, and perspectives throughout, and emphasizes interactions with the rest of mathematics. In addition to covering the basic concepts of mathematical logic and the fundamental material on completeness, compactness, and incompleteness, it devotes significant space to thorough introductions to the pillars of the modern subject: model theory, set theory, and computability. Requiring only a modest background of undergraduate mathematics, the text can be readily adapted for a variety of one- or two-semester courses at the upper-undergraduate or beginning-graduate level. Numerous examples reinforce the key ideas and illustrate their applications, and a wealth of classroom-tested exercises serve to consolidate readers' understanding. Comprehensive and engaging, this book offers a fresh approach to this enduringly fascinating and important subject.
Brief description: Joseph Mileti is Associate Professor in the Department of Mathematics and Statistics at Grinnell College, USA. He won the 2004 Sacks Prize from the Association of Symbolic Logic for the best doctoral dissertation in mathematical logic (worldwide) and leading experts have celebrated his original courses and materials taught at many universities.
Review Quotes: 'This book is a solid text for the first course on mathematical logic. It contains comprehensive and detailed material on the subject. Although the number of pages of the book is relatively large, any instructor who wants to adopt it as a text should not feel intimidated: the book is organized in such a way that an instructor can choose to emphasize a particular direction, such as set theory, model theory, computability theory, etc., for a one-semester course, or all of them for a one-year course, or anything in between. The proofs of the theorems in the book are gentle and often accompanied with rather illuminating modern examples. There is also a sufficient number of exercises for all sections with various levels of difficulty. Overall, this is an excellent textbook.' Renling Jin, MathSciNet