Provability, Computability and Reflection, Volume 75 (Studies in Logic and the Foundations of Mathematics) [Hardcover]

Lev D. Beklemishev (Author)

Book Description

Publication Date: February 26, 1973 | ISBN-10: 0444104844 | ISBN-13: 978-0444104847

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.

--This text refers to the Paperback edition.

Product Details

• Hardcover: 202 pages
• Publisher: Elsevier Science (February 26, 1973)
• Language: English
• ISBN-10: 0444104844
• ISBN-13: 978-0444104847
• Shipping Information: View shipping rates and policies
• Average Customer Review: 3.5 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #10,210,853 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

22 of 23 people found the following review helpful:

3.0 out of 5 stars Starts out a little rough, May 10, 2010

By 

Christopher Grant (Salem, UT USA) - See all my reviews
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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, October 7, 2009

By 

Dennis K. Morgan "dennisbigD" (Whitefish Bay, WI) - See all my reviews
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Amazon Verified Purchase

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.