# Sh:585

- Rabus, M., & Shelah, S. (2000).
*Covering a function on the plane by two continuous functions on an uncountable square—the consistency*. Ann. Pure Appl. Logic,**103**(1-3), 229–240. arXiv: math/9706223 DOI: 10.1016/S0168-0072(98)00053-0 MR: 1756147 -
Abstract:

It is consistent that for every function f:{\mathbb R}\times {\mathbb R}\rightarrow {\mathbb R} there is an uncountable set A\subseteq {\mathbb R} and two continuous functions f_0,f_1:D(A)\rightarrow {\mathbb R} such that f(\alpha,\beta)\in \{f_0(\alpha,\beta),f_1(\alpha,\beta)\} for every (\alpha,\beta) \in A^2, \alpha\not =\beta. - published version (12p)

Bib entry

@article{Sh:585, author = {Rabus, Mariusz and Shelah, Saharon}, title = {{Covering a function on the plane by two continuous functions on an uncountable square---the consistency}}, journal = {Ann. Pure Appl. Logic}, fjournal = {Annals of Pure and Applied Logic}, volume = {103}, number = {1-3}, year = {2000}, pages = {229--240}, issn = {0168-0072}, doi = {10.1016/S0168-0072(98)00053-0}, mrclass = {03E35 (26B05)}, mrnumber = {1756147}, mrreviewer = {Renling Jin}, doi = {10.1016/S0168-0072(98)00053-0}, note = {\href{https://arxiv.org/abs/math/9706223}{arXiv: math/9706223}}, arxiv_number = {math/9706223} }