Title
Axiomatic Set Theory (Dover Books on Mathematics),New
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One of the most pressingproblems of mathematics over the last hundred years has been the question: What is a number? One of the most impressive answers has been the axiomatic development of set theory. The question raised is: 'Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics?' Answering this question by means of the ZermeloFraenkel system, Professor Suppes' coverage is the best treatment of axiomatic set theory for the mathematics student on the upper undergraduate or graduate level.The opening chapter covers the basic paradoxes and the history of set theory and provides a motivation for the study. The second and third chapters cover the basic definitions and axioms and the theory of relations and functions. Beginning with the fourth chapter, equipollence, finite sets and cardinal numbers are dealt with. Chapter five continues the development with finite ordinals and denumerable sets. Chapter six, on rational numbers and real numbers, has been arranged so that it can be omitted without loss of continuity. In chapter seven, transfinite induction and ordinal arithmetic are introduced and the system of axioms is revised. The final chapter deals with the axiom of choice. Throughout, emphasis is on axioms and theorems; proofs are informal. Exercises supplement the text. Much coverage is given to intuitive ideas as well as to comparative development of other systems of set theory. Although a degree of mathematical sophistication is necessary, especially for the final two chapters, no previous work in mathematical logic or set theory is required.For the student of mathematics, set theory is necessary for the proper understanding of the foundations of mathematics. Professor Suppes in Axiomatic Set Theory provides a very clear and welldeveloped approach. For those with more than a classroom interest in set theory, the historical references and the coverage of the rationale behind the axioms will provide a strong background to the major developments in the field. 1960 edition.
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We provide a 2-year limited warranty, from the date of purchase for all our products.
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This warranty strictly does not cover damages that arose from negligence, misuse, wear and tear, or not in accordance with product instructions (dropping the product, etc.).
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Frequently Asked Questions
- Q: What is the main focus of 'Axiomatic Set Theory'? A: The book primarily addresses the foundational question of what constitutes a number and explores the axiomatic development of set theory, particularly through the Zermelo-Fraenkel system.
- Q: Who is the author of 'Axiomatic Set Theory'? A: The author is Patrick Suppes, a renowned mathematician known for his contributions to mathematical logic and set theory.
- Q: What topics are covered in the book? A: The book covers basic paradoxes, history of set theory, axioms, relations, functions, equipollence, finite sets, cardinal numbers, finite ordinals, denumerable sets, and the axiom of choice.
- Q: Is any prior knowledge of set theory required to read this book? A: No prior work in mathematical logic or set theory is required, although some mathematical sophistication is necessary for the final chapters.
- Q: What is the publication date and edition of this book? A: The book was published on June 1, 1972, and is the first edition.
- Q: How many pages are in 'Axiomatic Set Theory'? A: The book contains a total of 288 pages.
- Q: What is the condition of the book? A: The book is listed as 'New', indicating it is in pristine condition and has not been previously owned.
- Q: What type of binding does this book have? A: The book is available in paperback binding.
- Q: Who is this book intended for? A: This book is designed for mathematics students at the upper undergraduate or graduate level, as well as those with a deeper interest in the foundations of mathematics.
- Q: Are there exercises included in the book? A: Yes, exercises are included to supplement the text and reinforce the concepts discussed.