Editing Forcing (mathematics) (section)

{{Short description|Technique invented by Paul Cohen for proving consistency and independence results}}
{{for|the use of forcing in [[recursion theory]]|Forcing (computability)}}
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In the mathematical discipline of [[set theory]], '''forcing''' is a technique for proving [[consistency]] and [[independence (mathematical logic)|independence]] results. Intuitively, forcing can be thought of as a technique to expand the set theoretical [[universe (mathematics)|universe]] <math>V</math> to a larger universe <math>V[G]</math> by introducing a new "generic" object <math>G</math>.

Forcing was first used by [[Paul Cohen (mathematician)|Paul Cohen]] in 1963, to prove the independence of the [[axiom of choice]] and the [[continuum hypothesis]] from [[Zermelo–Fraenkel set theory]]. It has been considerably reworked and simplified in the following years, and has since served as a powerful technique, both in set theory and in areas of [[mathematical logic]] such as [[recursion theory]]. [[Descriptive set theory]] uses the notions of forcing from both recursion theory and set theory. Forcing has also been used in [[model theory]], but it is common in model theory to define [[generic filter|genericity]] directly without mention of forcing.