A variation on the method of forcing can also be used to demonstrate the consistency and unprovability of the axiom of choice, i . e ., that the axiom of choice is independent of ZF . The consistency of choice can be ( relatively ) easily verified by proving that the inner model L satisfies choice . ( Thus every model of ZF contains a submodel of ZFC, so that Con ( ZF ) implies Con ( ZFC ) . ) Since forcing preserves choice, we cannot directly produce a model contradicting choice from a model satisfying choice.
