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Basic Set Theory (Dover Books on Mathematics), by Azriel Levy
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Although this book deals with basic set theory (in general, it stops short of areas where model-theoretic methods are used) on a rather advanced level, it does it at an unhurried pace. This enables the author to pay close attention to interesting and important aspects of the topic that might otherwise be skipped over. Written for upper-level undergraduate and graduate students, the book is divided into two parts. The first covers pure set theory, including the basic notions, order and well-foundedness, cardinal numbers, the ordinals, and the axiom of choice and some of its consequences. The second part deals with applications and advanced topics, among them a review of point set topology, the real spaces, Boolean algebras, and infinite combinatorics and large cardinals. A helpful appendix deals with eliminability and conservation theorems, while numerous exercises supply additional information on the subject matter and help students test their grasp of the material. 1979 edition. 20 figures.
- Sales Rank: #1660511 in eBooks
- Published on: 2012-06-11
- Released on: 2012-06-11
- Format: Kindle eBook
About the Author
Levy, Institute of Mathematics, The Hebrew University of Jerusalem.
Most helpful customer reviews
1 of 1 people found the following review helpful.
a good knowledge of first order logic is almost required to ...
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OK, lets get this settled first-not for beginners! Second, a good knowledge of first order logic is almost required to understand his approach to classes versus sets and controlling the paradoxes which occur in naive set theory. Levy is a world renown expert in set theory but the book exposes his pedagogical strengths and weaknesses. At times he can be delightfully clear, "...this assumption which we get free of charge is called the induction hypothesis", and at other times woefully foggy, "much of set theory is concerned with what is meant by this and so on". Much is covered including applications of set theory in normal mathematical practice and much is left out such as examples. I have a mathematical background and use the book for self study in my retirement and find it what I would call pleasantly challenging, and I keep rewriting sections to make it clearer.
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