GROUPWISE DENSITY AND THE COFINALITY OF THE INFINITE SYMMETRICAL GROUP

We study the relationship between the cofinality c(Sym(w)) of the infi nite symmetric group and the cardinal invariants u and g. In particula r, we prove the following two results. Theorem 0.1. It is consistent w ith ZFC that there exists a simple P-w1-point and that c(Sym(w)) = w(2 ) = 2(w). Theorem 0.2. If there exist both a simple P-w1-point and a P -w2-point, then c(Sym(w)) = w(1).