Clubsuit
In mathematics, and particularly in axiomatic set theory, ♣S is a family of combinatorial principles that are a weaker version of the corresponding ◊S; it was introduced in 1975.Definition
For a given cardinal number and a stationary set, is the statement that there is a sequence such that
is usually written as just.♣ and ◊
It is clear that ◊ ⇒ ♣, and it was shown in 1975 that ♣ + CH ⇒ ◊; however, Saharon Shelah gave a proof in 1980 that there exists a model of ♣ in which CH does not hold, so ♣ and ◊ are not equivalent.
