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'''Forcing''' in [[recursion theory]] is a modification of [[Paul Cohen (mathematician)|Paul Cohen's]] original [[set theory|set-theoretic]] technique of [[forcing (set theory)|forcing]] to deal with the effective concerns in [[recursion theory]]. Conceptually the two techniques are quite similar: in both one attempts to build [[generic set|generic]] objects (intuitively objects that are somehow 'typical') by meeting dense sets. Both techniques are described as a relation (customarily denoted <math>\Vdash</math>) between 'conditions' and sentences. However, where set-theoretic forcing is usually interested in creating objects that meet every dense set of conditions in the ground model, recursion-theoretic forcing only aims to meet dense sets that are arithmetically or hyperarithmetically definable. Therefore, some of the more difficult machinery used in set-theoretic forcing can be eliminated or substantially simplified when defining forcing in recursion theory. But while the machinery may be somewhat different, recursion-theoretic and set-theoretic forcing are properly regarded as an application of the same technique to different classes of formulas.
==Terminology==
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