Modern Mathematical Logic

This book, meant for undergraduate mathematics students and teachers, introduces algebraic number theory through problems from ordinary number theory that can be solved with the help of algebraic numbers, using a suitable generalization of unique prime factorization. The material is motivated by weaving historical information throughout.

List of contents

Preface; Acknowledgements; 1. Introduction; 2. Induction and recursion; 3. Propositional logic; 4. First-order logic: languages and structures; 5. Relationships between structures; 6. Implication and compactness; 7. Model theory; 8. Axiomatic set theory; 9. Ordinals, cardinals, and choice; 10. Set-theoretic methods in model theory; 11. Computable sets and functions; 12. Logic, computation, and incompleteness; Appendix: mathematical background; References; Index.

About the author

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.

Product details

• Authors: Joseph Mileti, Joseph (Grinnell College Mileti
• Publisher: Cambridge University Press ELT
• Languages: English
• Product format: Hardback
• Released: 31.08.2022
• EAN: 9781108833141
• ISBN: 978-1-108-83314-1
• No. of pages: 550
• Series: Cambridge Mathematical Textbooks; Cambridge Mathematical Textboo
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Basic principles; Non-fiction book > Philosophy, religion > Philosophy: general, reference works; PHILOSOPHY / Logic, MATHEMATICS / Logic, Mathematical logic, Philosophy: logic