Lorenz Halbeisen,Regula Krapf
Goedel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics
Goedel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics
YOU SAVE £7.09
- Condition: Brand new
- UK Delivery times: Usually arrives within 2 - 3 working days
- UK Shipping: Fee starts at £2.39. Subject to product weight & dimension
Couldn't load pickup availability
Excellent- More about Goedel's Theorems and Zermelo's Axioms: A Firm Foundation of Mathematics
This book provides a comprehensive introduction to the foundations of mathematics, covering logical logic, model theory, Gödels theorems, and modern axiomatic set theory. It is suitable for undergraduate mathematics students and is intended for a one or two-semester introductory course.
Format: Paperback / softback
Length: 236 pages
Publication date: 17 October 2021
Publisher: Springer Nature Switzerland AG
This comprehensive text offers a concise and self-contained introduction to the fundamental principles of mathematics. The first part delves into the realm of mathematical logic, encompassing essential concepts such as logical axioms, formal proofs, and the fundamentals of model theory. Building upon this foundation, the authors present detailed proofs of Gödels classical completeness and incompleteness theorems. In particular, the book includes a comprehensive proof of Gödels second incompleteness theorem, which asserts that it is impossible to prove the consistency of arithmetic within its axioms.
The final part of the book focuses on introducing modern axiomatic set theory, based on the Zermelos axioms. It includes a presentation of Gödels constructible universe of sets, a concept that plays a central role in this branch of mathematics. Throughout the book, a recurring theme emerges: the exploration of standard and non-standard models of various theories, including Peano arithmetic, Presburger arithmetic, and the real numbers.
Designed for undergraduate mathematics students, this text serves as an ideal resource for a one or two-semester introductory course in logic and set theory. Each chapter concludes with a comprehensive list of exercises, designed to reinforce the key concepts discussed and enhance the understanding of the subject matter. Whether you are a student seeking to deepen your knowledge of mathematics or a professional looking to expand your expertise in this field, this book is an invaluable guide to the foundations of mathematics.
Weight: 385g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030522810
Edition number: 1st ed. 2020
This item can be found in:
UK and International shipping information
UK and International shipping information
UK Delivery and returns information:
- Delivery within 2 - 3 days when ordering in the UK.
- Shipping fee for UK customers from £2.39. Fully tracked shipping service available.
- Returns policy: Return within 30 days of receipt for full refund.
International deliveries:
Shulph Ink now ships to Australia, Canada, France, Ireland, Italy, Germany, Spain, Netherlands, New Zealand, United States of America, Belgium, India, United Arab Emirates.
- Delivery times: within 5 - 10 days for international orders.
- Shipping fee: charges vary for overseas orders. Only tracked services are available for international orders.
- Customs charges: If ordering to addresses outside the United Kingdom, you may or may not incur additional customs and duties fees during local delivery.
