On uniformly antisymmetric functions
逻辑
2016-09-06 v1
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
引用
@article{arxiv.math/9308222,
title = {On uniformly antisymmetric functions},
author = {Peter Komjath and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9308222},
year = {2016}
}