Forcing

Forcing is a proof technique of Zermelo-Fraenkel Set Theory. The technique was invented by Paula Cohen in 1962 to prove that the Axiom of Choice and Continuum hypothesis are independent in Zermelo-Fraenkel Set Theory (ZFC). It has since been used by set theorists to show the independence of many axioms and hypotheses, including the existence of large cardinals, König's lemma, and the Schröder-Bernstein theorem. Logicians hope that by iterating the forcing technique, perhaps transfinitely, they may be able to demonstrate the consistency of ZFC.