Mathematical Logic and Computation
£59.99
- Author: Jeremy Avigad, Carnegie Mellon University, Pennsylvania
- Date Published: November 2022
- availability: Available
- format: Hardback
- isbn: 9781108478755
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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.
Read more- A single uniform presentation of mathematical logic from the syntactic point of view, covering all core areas of the subject
- Highlights the aspects of mathematical logic that are fundamental to computer science
- Examples and exercises make it a suitable introduction for graduate students and advanced undergraduates
Reviews & endorsements
'Avigad provides a much needed introduction to mathematical logic that foregrounds the role of syntax and computability in our understanding of consistency and inconsistency. The result provides a jumping off point to any of the fields of modern logic, not only teaching the technical groundwork, but also providing a window into how to think like a logician.' Henry Towsner, University of Pennsylvania
See more reviews'This book by one of the most knowledgeable researchers in the field covers a remarkably broad selection of material without sacrificing depth. Its clear organization and unified approach - focused on a syntactic approach and on the role of computation - make it suitable for a wide range of introductory logic sequences at the upper-level undergraduate and graduate level, as well as a valuable resource for background material in more advanced logic courses.' Denis Hirschfeldt, University of Chicago
'… 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
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×Product details
- Date Published: November 2022
- format: Hardback
- isbn: 9781108478755
- length: 450 pages
- dimensions: 263 x 182 x 28 mm
- weight: 1.18kg
- availability: Available
Table of Contents
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.
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