Comprehensive in its selection of topics and results, this self-contained text examines the relative strengths and the consequences of the axiom of choice. Subjects include consistency and independence, permutation models, and examples and counterexamples of the axiom's use. Each chapter contains several problems and concludes with some historical remarks. 1973 edition.
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22 of 23 people found the following review helpful:
3.0 out of 5 stars
Starts out a little rough,
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This review is from: The Axiom of Choice (Dover Books on Mathematics) (Paperback)
(1) The second inequality on page 3, while true, is apparently only accidentally so, because the set on the right is not a subset of the set on the left. Changing [0,1] to [0,2] fixes this.
(2) The first reference to "rotations" on page 5 needs to be "nontrivial rotations"; otherwise, Q is the entire sphere, rather than a countable subset. (If you insist that rotations are automatically nontrivial, then the claim on page 4 that they can form a group is false.) (3) X^i on the fourth line of the proof of Lemma 1.5 needs to be X_1 instead. (4) The proof of Theorem 1.2 uses S to stand for two different things: a sphere and a countable subset thereof. (5) The point p is supposed to be an arbitrary point in S's cone but outside of C's cone. If the S here is supposed to be the uncountable S, then this doesn't guarantee that the right-hand side of (1.7) is a disjoint union as apparently intended, but if the S here is the countable S, then we're trying to choose p from an empty set. I'm guessing that the countable S is intended, and that p is supposed to be in C's cone but outside S's cone, not the other way around. These errors occur in the first ten pages of this book. Based on this small sample size, I'm finding it difficult to motivate myself to read any further. Sometimes buying an inexpensive, uncorrected Dover reprint isn't such a bargain.
7 of 17 people found the following review helpful:
4.0 out of 5 stars
Axiom of Choice,
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This review is from: The Axiom of Choice (Dover Books on Mathematics) (Paperback)
Good book if you are trying to understand where the field of Mathematics is going: from Set Theory (Cantor & Godel), to modern math going forward. High School and College math skills necessary to grasp hard concepts. However, a good read for lay Mathematicians.
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