ABSTRACT
Forcing was invented by Paul Cohen and first used in 1963 to show that Cantor’s Continuum Hypothesis (CH) cannot be decided from what we know to be true about sets. Hopefully you will remember CH from our earlier Remarks 3.1.16 and 8.2.9. More precisely, what Cohen did was devise a way of building a model of the usual axioms of set theory — that is, of the system ZFC of Zermelo-Fraenkel set theory with the Axiom of Choice — and forcing it to be a model in which CH was not true. Since Go¨del had already built a model of ZFC — specifically the universe of sets constructible from the usual set theoretic operations — in which CH is true, neither CH nor its negation could possibly be provable within ZFC.
