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On the combinatorial properties of Blackwell spaces. (English) Zbl 0575.28001

A separable metric space X is called Blackwell if whenever f:X\(\to^{1- 1}{\mathbb{R}}\) is Borel measurable, then f is a Borel isomorphism. It has been shown that under Martin’s Axiom and negation of Continuum Hypothesis (CH) that this property is not preserved under intersections with the analytic set and Cartesian products with a Borel set. Recently Rae M. Shortt (preprint) has constructed similar examples under CH.

MSC:

28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets
03E15 Descriptive set theory
03E50 Continuum hypothesis and Martin’s axiom
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