Abstract
We prove that the existence of a Borel lower density operator (a Borel lifting) with respect to the sigma -ideal of countable sets, for an uncountable Polish space, is equivalent to CH. One of the implications is known (due to K. Musiał) and the remaining implication is derived from a general abstract result dealing with the negation of GCH. We observe that there is no lower density Borel operator with respect to the sigma -ideal of countable sets, whose range is of bounded level in the Borel hierarchy.
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