A space with only Borel subsets

by Shelah. [Sh:730]
Periodica Math Hungarica, 2000
Miklos 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 MA_kappa every subspace of the reals of cardinality kappa has the property that all subsets are F_sigma however Martin's axiom also implies that these subsets are meager. Here we answer Laczkovich' question.


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