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Set Theory: An Introduction, by Robert L. Vaught
Download Set Theory: An Introduction, by Robert L. Vaught
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By its nature, set theory does not depend on any previous mathematical knowl edge. Hence, an individual wanting to read this book can best find out if he is ready to do so by trying to read the first ten or twenty pages of Chapter 1. As a textbook, the book can serve for a course at the junior or senior level. If a course covers only some of the chapters, the author hopes that the student will read the rest himself in the next year or two. Set theory has always been a sub ject which people find pleasant to study at least partly by themselves. Chapters 1-7, or perhaps 1-8, present the core of the subject. (Chapter 8 is a short, easy discussion of the axiom of regularity). Even a hurried course should try to cover most of this core (of which more is said below). Chapter 9 presents the logic needed for a fully axiomatic set th~ory and especially for independence or consistency results. Chapter 10 gives von Neumann's proof of the relative consistency of the regularity axiom and three similar related results. Von Neumann's 'inner model' proof is easy to grasp and yet it prepares one for the famous and more difficult work of GOdel and Cohen, which are the main topics of any book or course in set theory at the next level.
- Sales Rank: #2627385 in Books
- Brand: Brand: Birkhäuser
- Published on: 2007-10-24
- Original language: English
- Number of items: 1
- Dimensions: 9.00" h x .41" w x 6.00" l, .61 pounds
- Binding: Paperback
- 167 pages
- Used Book in Good Condition
Review
"One of [the book's] strengths is the author's voice. His prose is clear and correct...The text is quite concise."
--Mathematical Reviews
"The volume is in a clear and interesting style and is highly recommended to undergraduate students of mathematics as well as philosophy."
--Acta Sci. Math. (on the first edition)
From the Back Cover
This book corresponds to a view of the subject from someone who has thought deeply about this and many other aspects of mathematical logic. The second edition has been expanded to include selected solutions to the problems, increasing its usefulness as a teaching tool.
Most helpful customer reviews
5 of 7 people found the following review helpful.
geek review was uninformed
By 39mmb
The Geek review was unfair and uninformed. All books are written from the point of view of the background of the author and Robert Vaught was a logician so naturally this introduction to set theory was written from the perspective of a logician and a great one at that. The author places great stress on being intuitive and natural while leaving to the reader things he ought to be able to figure out for himself. The book does require a careful and thoughtful reading but the reward is many insights contained in no other book on this subject. For example, the sections on definition by induction are as clearly written as I have ever seen. This book grabs the replacement axion or principle up front and treats it as obvious as any other axion contrary to the majority of set theory books. As the author says, he leaves well ordering to the last as he finds the proofs related to it more difficult as Cantor himself did. I could go on and on, but to summarize, this book is a goldmine of information on sets and should be revered. Those who think otherwise just aren't up to learning the basics with true understanding. As for the minor point of relying of the index of Frankel for the references, this was standard practice in his day and is a minor flaw.
0 of 1 people found the following review helpful.
Great!
By Duohead
Short and sweet.
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