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Axiomatic Set Theory
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Showing 1-2 of 2 reviews(3 star)show all reviews
on October 3, 2003
This is a basic introduction to axiomatic set theory. You dont need much experience with informal set theory or formal logic to begin it. The book is rigorous and follows a definition - theorem - proof format, broken with clear exposition and historical notes. Enough formal mathematical logic is introduced only to express the axioms (that is, formal proof systems are not used or discussed). He uses the ZF (Zermelo/Fraenkel) system and gives footnote comparisons to the NBG (von Neumann/Bernays/Godel) system. In chapter 4 he introduces a special axiom (outside of ZF) to simplify the development of cardinal arithmetic, and this involves the addition of a new primitive notion. All theorems relying on this special axiom are clearly marked. While this admirably allows Suppes to avoid employing the axiom of choice or developing a much more complicated strictly ZF-based construction of the cardinals, it does make the book unacceptable for more advanced readers. In chapter 6 he gives a detailed construction of the rational numbers and the real numbers (using Cauchy sequences). He uses only the axiom of separation until the axiom of replacement becomes necessary. He does a good job explaining why each axiom is needed and how it arose historically. The book is comparable to Monk's _Introduction to Set Theory_, though a little easier and less advanced.
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on February 27, 2000
I skim this book one day while looking for some reference books at my local bookstore.The clarity of the book makes it a good book for complementing set theory courses.The examples are given in a consice manner without obstructing the learning material to the readers. However, the lack of answers to the given problems makes the book unfitting to first time readers who may want to learn the subject just for plain curiosity; none of the steps are hinted for solving any problem. It is unfair having to buy this book because readers buying this book are expected to be experts in the field. Rather, it should also consider general science readers who have interest for the subject and want to learn the material. I think having full answers to problems allows all readers to have a good understanding of the subject at hand since it clarifies the bridge of ideas that mathematicians are trying to let the world see. Furthermore, it motivates readers to critically think challenging problems once enough practice has been establish through the ones with answers. However, because there is a lack of communication and guidance to achieve a full census with the subject, this book has a mild sour taste. So in hopes that the author of this book improves the book for the benefit of his readers, "Please provide answers next time."
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