Mathematical Logic and Computation

A thorough introduction to the fundamental methods and results in mathematical logic, and its foundational role in computer science.

Jeremy Avigad (Author)

9781108478755, Cambridge University Press

Hardback, published 24 November 2022

450 pages
26.3 x 18.2 x 2.8 cm, 1.18 kg

'… an excellent addition to the literature, with plenty more than enough divergences and side-steps from the more well-trodden paths through the material to be consistently interesting … this is most certainly a book to make sure your library gets.' Peter Smith, Logic Matters

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.

Preface
1. Fundamentals
2. Propositional Logic
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.

Subject Areas: Computer architecture & logic design [UYF], Mathematical theory of computation [UYA], Mathematical logic [PBCD]