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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.
Preface.
Acknowledgments.
Introduction.
Induction and Recursion.
Propositional Logic.
First-Order Logic: Languages and Structures.
Relationships between Structures.
Implication and Compactness.
Model Theory.
Axiomatic Set Theory.
Ordinals, Cardinals, and Choice.
Set-Theoretic Methods in Model Theory.
Computable Sets and Functions.
Logic, Computation, and Incompleteness.
Appendix: Mathematical Background.
Bibliography.
List of Notation.
Index