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Discovering Modern Set Theory. I: The Basics (Graduate Studies in Mathematics, Vol 8) (Pt.1) Hardcover – Unabridged, December 5, 1995

ISBN-13: 978-0821802663 ISBN-10: 0821802666

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Discovering Modern Set Theory. I: The Basics (Graduate Studies in Mathematics, Vol 8) (Pt.1) + Discovering Modern Set Theory. II: Set-Theoretic Tools for Every Mathematician (Graduate Studies in Mathematics, Vol. 18)
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Product Details

  • Series: Graduate Studies in Mathematics (Book 8)
  • Hardcover: 210 pages
  • Publisher: American Mathematical Society (December 5, 1995)
  • Language: English
  • ISBN-10: 0821802666
  • ISBN-13: 978-0821802663
  • Product Dimensions: 0.8 x 7.5 x 10.5 inches
  • Shipping Weight: 1.2 pounds (View shipping rates and policies)
  • Average Customer Review: 5.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Best Sellers Rank: #749,625 in Books (See Top 100 in Books)

Editorial Reviews

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"These books aim to support first courses in rigorous set theory ... are thoroughly competent: well-organized, scrupulous in pointing out both mathematical and philosophical difficulties, carefully graded from relatively straightforward beginnings to demanding conclusions. The more interesting, and more demanding, approach is that of Just and Weese. These books are for those who not only want to learn mathematics, but want to think about mathematics." -- --Bulletin of the London Mathematical Society

"Well written and userfriendly." ---- Zentralblatt MATH

"Serious graduate students ... would profit from reading the book for the mathematical maturity they would gain in the process. The conversational, almost Socratic, style of exposition is well suited to giving students some insight into the process of doing mathematics as well as to the importance of asking the right questions ... Just and Weese's text would be ideally suited for ... students who are serious about studying set theory." ---- Journal of Symbolic Logic

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17 of 17 people found the following review helpful By A Reader on December 11, 2009
Format: Hardcover
Set theory presents many unusual challenges to the mathematician who wishes to pursue independent study of the subject at an advanced level. All mathematicians learn enough "naive" set theory to get by in their undergraduate and graduate coursework, and there is no shortage of good introductory texts in that subject. But when one decides to take the next step and study more formal, axiomatic set theory (specifically, Zermelo-Fraenkel set theory with the Axiom of Choice, or ZFC), the situation becomes far more challenging.

The primary problem is the difficult, circular relationship between formal mathematical logic and axiomatic set theory. One simply cannot attempt a serious study of ZFC as a formal system without having the requisite background in first-order mathematical logic; but one quickly learns that it is impossible to understand any of the good introductions to mathematical logic without having a considerable background in not-so-naive set theory! Set theory serves a perplexing dual role as (1) an example of a formal axiomatic system of considerable interest in its own right, and (2) the source of all the formal models than one builds in mathematical logic to show that various axiomatic systems are consistent. The often-made claim that all or nearly all of mathematics can be "embedded" in ZFC indicates to the student that this particular formal system has a very privileged role; it can be extremely difficult to understand precisely how this "embedding" is to unfold, and how one can use one axiomatic system (ZFC) to produce models for other axiom systems, thereby demonstrating their consistency.
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