Syllabus
Axiomatization of set theory: Zermelo-Frankel, axioms of Gödel and Bernays
Independent formulas, consistency and equiconsistecy of theories
Models of set theory, model class, extension of transitive model, absolute formulas
Ultrapower, measurable cardinal number, elementary injection, supercompact cardinal number
Generic filter, generic extension of transitive model, boolean names, forcing
Martin axiom, PFA (Proper forcing axiom), Martin's maximum
Examples of forcing: addition of real number, continuum can be arbitrary huge, collapsing of cardinal numbers, Levy's collaps
Suslin hypothesis
Iteration, consistency of Martin axiom
Annotation
Forsing is a method for constructions of models of set theory.
It is a method for verifying unprovability or consistency of various mathematical statements.