Strongly almost disjoint families, II
Abstract
The relations M(kappa,lambda,mu)->B [resp. B(sigma)] meaning that if A subset [kappa]lambda with |A|=kappa is mu-almost disjoint then A has property B [resp. has a sigma-transversal] had been introduced and studied under GCH by Erdos and Hajnal in 1961. Our two main results here say the following: Assume GCH and rho be any regular cardinal with a supercompact [resp. 2-huge] cardinal above rho. Then there is a rho-closed forcing P such that, in VP, we have both GCH and M(rho(+rho+1),rho+,rho) not-> B [resp. M(rho(+rho+1),lambda,rho) not-> B(rho+) for all lambda =< rho(+rho+1)].
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