Editing Forcing (mathematics) (section)

== Boolean-valued models ==
{{main article|Boolean-valued model}}

Perhaps more clearly, the method can be explained in terms of Boolean-valued models. In these, any statement is assigned a [[truth value]] from some complete atomless [[Boolean algebra (structure)|Boolean algebra]], rather than just a true/false value. Then an [[ultrafilter]] is picked in this Boolean algebra, which assigns values true/false to statements of our theory. The point is that the resulting theory has a model that contains this ultrafilter, which can be understood as a new model obtained by extending the old one with this ultrafilter. By picking a Boolean-valued model in an appropriate way, we can get a model that has the desired property. In it, only statements that must be true (are "forced" to be true) will be true, in a sense (since it has this extension/minimality property).