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Each Borel set of a Polish space is classified in the '''[[Borel hierarchy]]''' based on how many times the operations of countable union and complementation must be used to obtain the set, beginning from open sets. The classification is in terms of [[countable set|countable]] [[ordinal number]]s. For each nonzero countable ordinal α there are classes <math>\mathbf{\Sigma}^0_\alpha</math>, <math>\mathbf{\Pi}^0_\alpha</math>, and <math>\mathbf{\Delta}^0_\alpha</math>.
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* A set is declared to be <math>\mathbf{\Pi}^0_\alpha</math> if and only if its complement is <math>\mathbf{\Sigma}^0_\alpha</math>.
* A set ''A'' is declared to be <math>\mathbf{\Sigma}^0_\delta</math>, δ > 1, if there is a sequence ⟨ ''A''<sub>''i''</sub> ⟩ of sets, each of which is <math>\mathbf{\Pi}^0_{\lambda(i)}</math> for some λ(''i'') < δ, such that <math>A = \bigcup A_i</math>.
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