Sh:668

• Shelah, S. (2004). Anti-homogeneous partitions of a topological space. Sci. Math. Jpn., 59(2), 203–255. arXiv: math/9906025 MR: 2062196
• 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.
• Version 2006-03-11_10 (70p) published version (53p)

@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}},
 specialissue = {Special issue on set theory and algebraic model theory},
 arxiv_number = {math/9906025},
 keyword = {set theory, general topology, partition calculus, pcf
theory}
}