Lectures in Set Theory

Inhaltsverzeichnis

• 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.