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'''Forcing''' in [[computability 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 computability concerns.
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The idea is that our language should express facts about the object we wish to build with our forcing construction.
== Forcing relation ==
The forcing relation <math>\Vdash</math> was developed by [[Paul Cohen]], who introduced forcing as a technique for proving the independence of certain statements from the standard axioms of set theory, particularly the [[continuum hypothesis]] (CH).
The notation <math>V \Vdash \phi</math> is used to express that a particular condition or generic set forces a certain proposition or formula <math>\phi</math> to be true in the resulting forcing extension. Here's <math>V</math> represents the original universe of sets (the ground model), <math>\Vdash</math> denotes the forcing relation, and <math>\phi</math> is a statement in set theory.
When <math>V \Vdash \phi</math>, it means that in a suitable forcing extension, the statement <math>\phi</math> will be true.
== References ==
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|___location=Amsterdam, New York, and Oxford
|series=Studies in Logic and the Foundations of Mathematics
|pages=1078–1079
|doi=10.2307/2273928
|volume=105
|jstor=2273928
|s2cid=118376273
}}
*{{Cite book
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