D ec 1 99 8 STRONGLY ALMOST DISJOINT FAMILES
نویسندگان
چکیده
The relations M(κ, λ, µ) → B [resp. B(σ)] meaning that if A ⊂ [κ] λ with |A| = κ is µ-almost disjoint then A has property B [resp. has a σ-transversal] had been introduced and studied under GCH in [EH]. Our two main results here say the following: Assume GCH and ̺ be any regular cardinal with a supercompact [resp. 2-huge] cardinal above ̺. Then there is a ̺-closed forcing P such that, in V P , we have both GCH and M(̺ (+̺+1) , ̺ + , ̺) B [resp. M(̺ (+̺+1) , λ, ̺) B(̺ +) for all λ ≤ ̺ (+̺+1) ]. These show that, consistently, the results of [EH] are sharp. The necessity of using large cardinals follows from the results of [HJSh] and [BDJShSz].
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