List of forcing notions
In mathematics, forcing is a method of constructing new models M[G] of set theory by adding a generic subset G of a poset P to a model M. The poset P used will determine what statements hold in the new universe (the 'extension'); to force a statement of interest thus requires construction of a suitable P. This article lists some of the posets P that have been used in this construction. == Notation == P is a poset with order < V is the universe of all sets M is a countable transitive model of set theory G is a generic subset of P over M. == Definitions == P satisfies the countable chain condition if every antichain in P is at most countable.