# Sh:502

• Komjáth, P., & Shelah, S. (1993). On uniformly antisymmetric functions. Real Anal. Exchange, 19(1), 218–225.
• Abstract:
We show that there is always a uniformly antisymmetric f:A\to\{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\to\omega with |S_x|\leq 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\to\{0,1,2,3\} such that S_x is always finite, but no such function with finite range on R exists
• Version 1993-08-27_10 (7p)
Bib entry
@article{Sh:502,
author = {Komj{\'a}th, P{\'e}ter and Shelah, Saharon},
title = {{On uniformly antisymmetric functions}},
journal = {Real Anal. Exchange},
fjournal = {Real Analysis Exchange},
volume = {19},
number = {1},
year = {1993},
pages = {218--225},
issn = {0147-1937},
mrnumber = {1268847},
mrclass = {26A15 (03E50 04A20)},
note = {\href{https://arxiv.org/abs/math/9308222}{arXiv: math/9308222}},
arxiv_number = {math/9308222}
}