Forcing (mathematics)

hypothesis that no set has a cardinality between that of the integers and that of the real numbers

in set theory, a technique for enlarging models of axioms of set theory (e.g. ZFC) by adjoining new elements, often used for proving consistency and independence results

collection of sets in which every two sets have the same intersection

mathematical lemma

condition in order theory and topology

set theory axiom that if 𝑃 is a proper forcing and 𝐷(𝛼) is a dense subset of 𝑃 for each 𝛼<ω₁, then there is a filter 𝐺⊆𝑃 such that 𝐷(𝛼)∩𝐺 is nonempty for all 𝛼<ω₁

in set theory, given a collection of dense open subsets of a poset, a filter that meets all sets in that collection