Sunflower (mathematics)

The lemma is a mathematical set of combinatorial set theory. It finds application in the development of the forcing method.

Statement

Let be a family of sets, and a further quantity. ie, a system with root, if the following holds:

• , The intersection of two sets of is constant.

The lemma now states: Every uncountable family of finite sets contains a überabzählbares system.

Generalization

The lemma can be generalized as follows: Let cardinal numbers with

• Is regular:
• For all true: (see cardinal arithmetic),

Then there is for every family with and for a system of cardinality. Putting and, we obtain the above special case.