# Sh:668

• Shelah, S. (2004). Anti-homogeneous partitions of a topological space. Sci. Math. Jpn., 59(2), 203–255.
• Abstract:
We prove the consistency (modulo supercompact) of a negative answer to Arhangelskii’s problem (some Hausdorff compact space cannot be partitioned to two sets not containing a closed copy of Cantor discontinuum). In this model we have CH. Without CH we get consistency results using a pcf assumption, close relatives of which are necessary for such results.
• published version (53p)
Bib entry
@article{Sh:668,
author = {Shelah, Saharon},
title = {{Anti-homogeneous partitions of a topological space}},
journal = {Sci. Math. Jpn.},
fjournal = {Scientiae Mathematicae Japonicae},
volume = {59},
number = {2},
year = {2004},
pages = {203--255},
issn = {1346-0862},
mrnumber = {2062196},
mrclass = {03E35 (03E02 03E04 03E55 54A35)},
note = {\href{https://arxiv.org/abs/math/9906025}{arXiv: math/9906025}},
arxiv_number = {math/9906025},
keyword = {set theory, general topology, partition calculus, pcf
theory},
specialissue = {Special issue on set theory and algebraic model theory}
}