Syllabus
Ordinal and cardinal arithmetic. The axiom of regularity. The cummulative hierarchy of sets.
Well-founded relations and induction. Collapsing theorems. Transitive models. Constructible sets.
Consistence of the axiom of choice and the generalization continuum hypothesis.
Ultrapowers and elementary embeddings. Measurable and inaccessible cardinals.
Bulean-valued models, generic extensions. Independence of the continuum hypothesis.
Non-regular set theory with strong choice and with the axiom of superuniversality. Nonstandard methods.
Applications.
Annotation
Ordinal and cardinal numbers, well-founded relations, isomorphism theorem, reflection principle. Transitive models, constructible sets, ultrapowers, measurable cardinals, Scott's theorem.
Forcing and Boolean-value models, a consistency of negation of the continuum hypothesis. Nonstandard set theory, axiom of superuniversality, elementary embedding of the universe into a transitive class, standard, internal and external sets.