Editing Set theory (section)

=== Forcing ===
{{Main|Forcing (mathematics)}}

[[Paul Cohen (mathematician)|Paul Cohen]] invented the method of ''[[forcing (mathematics)|forcing]]'' while searching for a [[model theory|model]] of [[ZFC]] in which the [[continuum hypothesis]] fails, or a model of ZF in which the [[axiom of choice]] fails. Forcing adjoins to some given model of set theory additional sets in order to create a larger model with properties determined (i.e. "forced") by the construction and the original model. For example, Cohen's construction adjoins additional subsets of the [[natural number]]s without changing any of the [[cardinal number]]s of the original model. Forcing is also one of two methods for proving [[consistency (mathematical logic)|relative consistency]] by finitistic methods, the other method being [[Boolean-valued model]]s.