Abstract
After P. S. Aleksandrov, Hausdorff, and M. Ya. Suslin proved in 1916-1917 that any uncountable Borel set, and even any uncountable A-set on the real line, contains a perfect subset, and thus has the cardinality of the continuum c = 2~o, one of the main problems in the descriptive set theory at that time was that of investigating the cardinality of CAsets (i.e., sets complementary to A-sets). The essence of this problem is the following:
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