The spectrum of partitions of a Boolean algebra
The spectrum of partitions of a Boolean algebra
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布尔代数的分区谱
DOI：
10.1007/s001530000065
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发表时间：
2001
影响因子：
0.3
通讯作者：
J. Monk
中科院分区：
文献类型：
--
作者：
J. Monk
我们引入一些符号，使我们的结果更容易表述。设κ， ν，µ是无限基数，使得ν≤µ≤κ。如果| A∩B|< ν，集合A和B ν-几乎不相交（ν-ad）。如果集合族A中的任意两个元素是ν-ad，则集合族A是ν-几乎不相交的（ν-ad）。现在设F是一个集合族，每个集合的大小至少为ν。我们说A是F的极大ν-几乎不相交（F, ν-mad），如果A是ν-ad，并且在F的ν-ad的子集中是极大的。相当于,一个是F-maximalν几乎不相交的如果一个⊆F,ν是广告,并为每个X∈F有X∩Y Y∈这样| |≥ν。而不是[κ] κ， κ-mad我们说κ-mad或κ- maximum almost disjoint。现在我们定义
We introduce some notation which will make it easier to state our results. Suppose that κ, ν, µ are infinite cardinals such that ν≤ µ≤ κ. Sets A and B are ν-almost disjoint (ν-ad) if| A∩ B|< ν. A family A of sets is ν-almost disjoint (ν-ad) if any two members of A are ν-ad. Now let F be a family of sets each of size at least ν. We say that A is F-maximal ν-almost disjoint (F, ν-mad) if A⊆ F, it is ν-ad, and it is maximal among subsets of F which are ν-ad. Equivalently, A is F-maximal ν-almost disjoint if A⊆ F, it is ν-ad, and for each X∈ F there is a Y∈ A such that| X∩ Y|≥ ν. Instead of [κ] κ, κ-mad we say κ-mad or κ-maximal almost disjoint. Now we define