MAD系列和SANE播放器
MAD Families and SANE Player
摘要：
我们抛出一些光的问题：是否有一个MAD家庭（=一个家庭的无限子集的N，任何两个的交集是有限的），这是完全可分的（即任何X subseteq N是包括在一个有限联盟的成员的家庭或包括一个成员的家庭）。证明了：（a）如果2^{aleph_0} < aleph_omega，则存在这样一个族;（b）如果不存在这样的族，则与pcf有关的某些情形成立，其一致性是大的。
英文摘要：
We throw some light on the question: is there a MAD family (= a family of infinite subsets of N, the intersection of any two is finite) which is completely separable (i.e. any X subseteq N is included in a finite union of members of the family or include a member of the family). We prove that it is hard to prove the consistency of the negation: (a) if 2^{aleph_0} < aleph_omega, then there is such a family (b) if there is no such families then some situation related to pcf holds whose consistency is large.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
