1998/12/18 by Andras Hajnal, Hajnal, Andras, Istvan Juhasz +3
Mathematics · #03E05 #03E35 #03E55 #04A20 #04A30 #FOS: Mathematics #Logic (math.LO) #math.LO #msc:03E05 #msc:03E35 #msc:03E55 #msc:04A20 #msc:04A30
paper · pdf · doi:10.48550/arxiv.math/9812114
published as Fund. Math. 163 No. 1 (2000) 13--23
arxiv created 1998/12/18 · arxiv updated 2009/11/30
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)].