Set Theory: An Introduction to Independence Proofs

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Set Theory: An Introduction to Independence Proofs is an important 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 exposit 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 really for beginners, but graduate students with some minimal experience in set theory and formal logic will find it a valuable self-teaching tool, particularly in regards 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.

[edit] References

• Kunen, Kenneth (1980). Set Theory: An Introduction to Independence Proofs. North-Holland. ISBN 0-444-85401-0.