# DISTINGUISHING PERFECT SET PROPERTIES IN SEPARABLE METRIZABLE SPACES

@article{Medini2016DISTINGUISHINGPS,
title={DISTINGUISHING PERFECT SET PROPERTIES IN SEPARABLE METRIZABLE SPACES},
author={Andrea Medini},
journal={The Journal of Symbolic Logic},
year={2016},
volume={81},
pages={166 - 180}
}
• Andrea Medini
• Published 1 May 2014
• Mathematics
• The Journal of Symbolic Logic
Abstract All spaces are assumed to be separable and metrizable. Our main result is that the statement “For every space X, every closed subset of X has the perfect set property if and only if every analytic subset of X has the perfect set property” is equivalent to b > ω1 (hence, in particular, it is independent of ZFC). This, together with a theorem of Solecki and an example of Miller, will allow us to determine the status of the statement “For every space X, if every Γ subset of X has the…
1 Citations

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