 | This article needs attention from an expert in mathematics or logic. The specific problem is: Article incomplete. (April 2021) |
Forcing in computability theory is a modification of Paul Cohen's original set-theoretic technique of forcing to deal with computability concerns.
Conceptually the two techniques are quite similar: in both one attempts to build generic objects (intuitively objects that are somehow 'typical') by meeting dense sets. Both techniques are described as a relation (customarily denoted ) 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, computability-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 computability. But while the machinery may be somewhat different, computability-theoretic and set-theoretic forcing are properly regarded as an application of the same technique to different classes of formulas.
