This technique's  rst major application was in proving the indepen- dence of   Zermelo-Fraenkel set theory from the axiom of choice and from the continuum hypothesis.
This technique uses the Löwenheim-Skolem theorem and the Mostowski col- lapsing theorem to ensure that objects in it are countable and transitive. This technique uses its namesake posets, which satisfy a splitting condition and are associated with a class of names. The original version of this technique is now called its rami ed version, which is distinguished from the newer unrami ed version. This technique's  rst major application was in proving the indepen- dence of   Zermelo-Fraenkel set theory from the axiom of choice and from the continuum hypothesis. For ten points, identify this technique of proof used in set theory and developed by Paul Cohen.
This technique uses the Löwenheim-Skolem theorem and the Mostowski col- lapsing theorem to ensure that objects in it are countable and transitive.
forcing