Clubsuit
Appearance
In
◊S; it was introduced in 1975 by Adam Ostaszewski.[1]
Definition
For a given cardinal number and a stationary set , is the statement that there is a sequence such that
- every Aδ is a cofinal subset of δ
- for every unbounded subset , there is a so 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 (since ◊ ⇒ CH).[2]
See also
References
- .
- .