On Property of Families of Sets

Abstract

A family of sets is said to have property if there exists a set B such that B ∩ F ≠ Ø and B ⊅ F for every F ∊ . Such a B will be called suitable with respect to F. It is known (see [3]) that for each positive integer n there exists a family of sets satisfying the following conditions:(a)|F| = n for each F ∊ (b)|F ∩ G| ≤ for F, G ∊ F ≠ G(c)does not have property