Set Theory: An Introduction to Independence Proofs

Set Theory: An Introduction to Independence Proofs is a textbook and reference work in set theory by Kenneth Kunen. It starts from basic notions, including the ZFC axioms, and quickly develops combinatorial notions such as trees, Suslin's problem, ◊, and Martin's axiom. It develops some basic model theory (rather specifically aimed at models of set theory) and the theory of Gödel's constructible universe L.

The book then proceeds to describe the method of forcing. Through exercises, the reader learns to apply the method to prove logical independence results in set theory.

This book is not suitable for beginners, but graduate students with some minimal experience in set theory and formal logic could find it a valuable self-teaching tool, particularly in regard to forcing. Some find it easier to read than a true reference work such as Thomas Jech's Set Theory. It is the standard textbook from which to learn forcing, though it has the disadvantage that the exposition of forcing relies somewhat on the earlier presentation of Martin's axiom, and the style is perhaps overly concise. John L. Bell's Set Theory: Boolean-Valued Models and Independence Proofs is an alternative, though it presents the topic from the standpoint of the more conceptually elegant though less easily used technique of Boolean-valued models of set theory. Jech's presentation is a hybrid of the former two styles.

Kunen totally rewrote the book for the 2011 edition (under the title "set theory"), including more model theory.

References

• Baumgartner, James E. (June 1986). "Set Theory. An Introduction to Independence Proofs by Kenneth Kunen". The Journal of Symbolic Logic 51 (2): 462–464. doi:10.2307/2274070.
• Henson, C. Ward (1984). "Set theory, An introduction to independence proofs by Kenneth Kunen". Bull. Amer. Math. Soc. 10: 129–131. doi:10.1090/S0273-0979-1984-15214-5.
• Kunen, Kenneth (1980). Set Theory: An Introduction to Independence Proofs. North-Holland. ISBN 0-444-85401-0. Zbl 0443.03021.
• Kunen, Kenneth (2011). Set theory. Studies in Logic 34. London: College Publications. ISBN 978-1-84890-050-9. MR 2905394. Zbl 1262.03001.