A space with only Borel subsets

Saharon Shelah

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A space with only Borel subsets

Saharon Shelah

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Abstract

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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BibTeX RIS

Saharon Shelah. 2000-09-05. A space with only Borel subsets. https://arxiv.org/abs/math/0009047

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