Descriptive set theory studies those subsets of topological spaces (called pointsets) which can be defined, by means of a list of specified operations including, e.g., complement, countable union and intersection, projection, beginning with open sets of the space. Classical descriptive set theory (DST) considers mainly sets in Polish (that is, separable metric) spaces, this is why we shall identify it here as Polish descriptive set theory.
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- “Hyperfinite” descriptive set theory
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