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arxiv: math/0009047 · v1 · pith:DHLLGJHPnew · submitted 2000-09-05 · 🧮 math.LO · math.GN

A space with only Borel subsets

Saharon Shelah This is my paper
classification 🧮 math.LO math.GN
keywords subsetsboreleverykappalaczkovichmeagerspaceanswer
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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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