关于一致反对称函数
On uniformly antisymmetric functions
摘要：
证明了如果A的子集R是可数的，则总有一致反对称f：A-> {0，1}.我们证明了连续统假设等价于存在一个f：R-> omega，其中对R中的每个x，|S_x| <= 1.如果连续统至少是aleph_n，则存在点x使得S_x至少有2^n-1个元素。我们还证明了存在函数f：Q-> {0，1，2，3}使得S_x总是有限的，但不存在这样的函数在R上具有有限值域
英文摘要：
We show that there is always a uniformly antisymmetric f:A-> {0,1} if A subset R is countable. We prove that the continuum hypothesis is equivalent to the statement that there is an f:R-> omega with |S_x| <= 1 for every x in R. If the continuum is at least aleph_n then there exists a point x such that S_x has at least 2^n-1 elements. We also show that there is a function f:Q-> {0,1,2,3} such that S_x is always finite, but no such function with finite range on R exists
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