Lectures in Set Theory : With Particular Emphasis on the Method of Forcing (Lecture Notes in Mathematics 217) (1971)

Formulas and classes.- Axioms of Zermelo-Fraenkel.- Ordinal numbers.- Cardinal numbers.- Finite sets.- Real numbers.- Axiom of choice.- Cardinal arithmetic.- Axiom of regularity.- Transitive models.- Constructible sets.- Consistency of AC and GCH.- More on transitive models.- Ordinal definability.- Remarks on complete boolean algebras.- The method of forcing and boolean - valued models.- Independence of the continuum hypothesis and collapsing of cardinals.- Two applications of boolean-valued models in the theory of boolean algebras.- Lebesgue measurability.- Suslin's problem.- Martin's axiom.- Perfect forcing.- Remark on ordinal definability.- Independence of AC.- Fraenkel-mostowski models.- Embedding of FM models in models of ZF.