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Set Theory and the Continuum Hypothesis (Dover Books on Mathematics)
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Top Customer Reviews
Although it is only 154 pages, it is remarkably wide-ranging, and has held up very well in the 37 years since it was first published. Cohen is a very good mathematical writer and his arrangement of the material is irreproachable. All the arguments are well-motivated, the number of details left to the reader is not too large, and everything is set in a clear philosophical context. The book is completely self-contained and is rich with hints and ideas that will lead the reader to further work in mathematical logic.
It is one of my two favorite math books (the other being Conway's "On Numbers and Games"). My copy is falling apart from extreme overuse.
Professor Cohen passed away in March of 2007, but thankfully this book remains as a testament to his genius. Originally trained as an analyst, he began working on the continuum hypothesis knowing almost nothing about logic or set theory. Within two years he mastered the subject and solved the greatest outstanding problem in the field (and arguably in all of mathematics). Read this book if you want to understand one of the deepest ideas in all of human thought.
This edition is a reproduction of the first edition. You might be shocked by the type-this is a plain, typewritten document with no illustrations (I find it charming)-but Paul Cohen's crystal clear prose makes the book eminently readable.
=WHAT YOU NEED=
This is a graduate level book but you don't need to be a graduate student in mathematics to understand it. You do need a laymen's interest in mathematics; for instance you should enjoy reading Euclid, Ian Stewart, Douglas Hoftstadter, Martin Gardner. If you've enjoyed Douglas Hofstadter's "Gödel, Escher, and Bach" then there is no reason you can't understand this book.
=WHAT IT DELIVERS=
First, Cohen gives a barebones but complete introduction to formal logic and logical notation.
Then he describes formal set theory, known as Zemerlo Frankel set theory, the foundation of all mathematics as it stands today.
Having spent half the book on the necessary background, Cohen arrives to his main topic, the Continuum Hypothesis and whether it is true or false.
=WHAT COHEN SAYS=
ST&CH proves that a long standing problem in mathematics (the Continuum Hypothesis) has no solution. What does this mean?
Most mathematicians believe in a scaled down version of Hilbert's Programme. Hilbert hoped that all of mathematics followed from a small collection of definitions and axioms, much like all of geometry was once believed to follow from Euclid's five axioms.Read more ›
The volume has very interesting prefatory memoir by Cohen in which he recounts how he was attracted to the Continuum Problem and his meetings with Kurt Gödel after he (Cohen) obtained his independence proof. There is also a nice introduction by the great logician Martin Davis.
Most Recent Customer Reviews
The mathematics content deserves a 6 star rating. It was a good surprise to find in this classic of Cohen such a fine exposition, clear and magnificently structured... Read morePublished 8 months ago by Eduardo Rego
This has been one of my favorite books over the years. Copies were hard to get. There was one at a library near my former workplace, which, unintuitively enough, was an Army post;... Read morePublished on February 4, 2013 by Dr. James V. Blowers
We used to think that if we could prove something existed with symbols, words, or diagrams, that it must exist. Read morePublished on October 28, 2012 by L. Hotchkiss
This book reminds me of the Russellian Principia.... To be filed in the list of unreadable books : books written by great mathematicians for their peers, professional... Read morePublished on October 13, 2011 by André Gargoura
I wasn't expecting an easy read, but I'll wait to tackle this after I've absorbed "The Joy of Sets". Read morePublished on July 24, 2011 by JC
Easiliy readable and very profound in content. Not only a must reading for researchers in set theory but also the best introduction in mathematical logic.Published on December 26, 2010 by Isao Nakano
It is a book that the most part of him is written in a naive form(not in formal logic).
You need a basic knowledge of Set Theory(like Halmos Book). Read more