Sh:502

• Komjáth, P., & Shelah, S. (1993). On uniformly antisymmetric functions. Real Anal. Exchange, 19(1), 218–225. arXiv: math/9308222 MR: 1268847
• 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)

@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}
}