### On uniformly antisymmetric functions

by Komjath and Shelah. [KoSh:502]

Real Analysis Exchange, 1993-1994

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

Back to the list of publications