On uniformly antisymmetric functions

Peter Komjath; Saharon Shelah

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On uniformly antisymmetric functions

Peter Komjath·Saharon Shelah

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Abstract

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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BibTeX RIS

Peter Komjath, Saharon Shelah. 1993-08-15. On uniformly antisymmetric functions. https://arxiv.org/abs/math/9308222

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