A more recent book on Set Theory:
Basic Set Theory—A. Shen, Independent University of Moscow, and N. K. Vereshchagin, Moscow State Lomonosov University—AMS, 2002, 116 pp., Softcover, ISBN-10: 0-8218-2731-6, ISBN-13: 978-0-8218-2731-4, List: US$24, All AMS Members: US$19.20, STML/17
By the way, the Shen’s book takes a different route to the Zorn’s lemma: first he introduces well-ordered sets, then uses tranfinite recursion to prove Zermelo’s theorem (that any set can be well-ordered), then he uses Zermelo’s theorem and tranfinite recursion to prove Zorn’s lemma. Thus the proof of Zorn’s lemma is reduced from two pages to a few lines. I personally found it easier to follow and remember.
Thanks for the review.
A more recent book on Set Theory: Basic Set Theory—A. Shen, Independent University of Moscow, and N. K. Vereshchagin, Moscow State Lomonosov University—AMS, 2002, 116 pp., Softcover, ISBN-10: 0-8218-2731-6, ISBN-13: 978-0-8218-2731-4, List: US$24, All AMS Members: US$19.20, STML/17
I found it in the American Mathematical Society for Student’s series, which is highly recommended on mathoverflow.com: http://www.ams.org/bookstore/stmlseries
Thanks for the recommendation! We’ll check it out.
By the way, the Shen’s book takes a different route to the Zorn’s lemma: first he introduces well-ordered sets, then uses tranfinite recursion to prove Zermelo’s theorem (that any set can be well-ordered), then he uses Zermelo’s theorem and tranfinite recursion to prove Zorn’s lemma. Thus the proof of Zorn’s lemma is reduced from two pages to a few lines. I personally found it easier to follow and remember.