Sh:730

• Shelah, S. (2000). A space with only Borel subsets. Period. Math. Hungar., 40(2), 81–84. arXiv: math/0009047 DOI: 10.1023/A:1010364023601 MR: 1805307
• Abstract:
  Miklós Laczkovich asked if there exists a Haussdorff (or even normal) space in which every subset is Borel yet it is not meager. The motivation of the last condition is that under {\rm MA}_\kappa every subspace of the reals of cardinality \kappa has the property that all subsets are {\rm F}_\sigma however Martin’s axiom also implies that these subsets are meager. Here we answer Laczkovich’ question.
• Version 2000-03-22_11 (3p) published version (4p)

@article{Sh:730,
 author = {Shelah, Saharon},
 title = {{A space with only Borel subsets}},
 journal = {Period. Math. Hungar.},
 fjournal = {Periodica Mathematica Hungarica. Journal of the J\'anos Bolyai Mathematical Society},
 volume = {40},
 number = {2},
 year = {2000},
 pages = {81--84},
 issn = {0031-5303},
 mrnumber = {1805307},
 mrclass = {03E35 (03E55 54H05)},
 doi = {10.1023/A:1010364023601},
 note = {\href{https://arxiv.org/abs/math/0009047}{arXiv: math/0009047}},
 arxiv_number = {math/0009047}
}