# 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} }

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…

## One Citation

### The onto mapping property of Sierpinski

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