# 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. - published version (4p)

Bib entry

@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}, doi = {10.1023/A:1010364023601}, mrclass = {03E35 (03E55 54H05)}, mrnumber = {1805307}, mrreviewer = {Jakub Jasi\'nski}, doi = {10.1023/A:1010364023601}, note = {\href{https://arxiv.org/abs/math/0009047}{arXiv: math/0009047}}, arxiv_number = {math/0009047} }