Mathematical Logic and Computation - Avigad, Jeremy

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Résumé :
This new book on mathematical logic by Jeremy Avigad gives a thorough introduction to the fundamental results and methods of the subject from the syntactic point of view, emphasizing logic as the study of formal languages and systems and their proper use. Topics include proof theory, model theory, the theory of computability, and axiomatic foundations, with special emphasis given to aspects of mathematical logic that are fundamental to computer science, including deductive systems, constructive logic, the simply typed lambda calculus, and type-theoretic foundations. Clear and engaging, with plentiful examples and exercises, it is an excellent introduction to the subject for graduate students and advanced undergraduates who are interested in logic in mathematics, computer science, and philosophy, and an invaluable reference for any practicing logician's bookshelf....

Biographie:
Carnegie Mellon University, Pennsylvania

Sommaire:
Preface; 1. Fundamentals; 2. Propositional; 3. Semantics of Propositional Logic; 4. First-Order Logic; 5. Semantics of First-Order Logic; 6. Cut Elimination; 7. Properties of First-Order Logic; 8. Primitive Recursion; 9. Primitive Recursive Arithmetic; 10. First-Order Arithmetic; 11. Computability 12. Undecidability and Incompleteness; 13. Finite Types; 14. Arithmetic and Computation; 15. Second-Order Logic and Arithmetic; 16. Subsystems of Second-Order Arithmetic; 17. Foundations; Appendix; References; Notation; Index.