Page "Arithmetical hierarchy" Paragraph 43
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* Every arithmetical subset of Cantor space of < sup >( or?
)</ sup > Baire space is a Borel set.
The lightface Borel hierarchy extends the arithmetical hierarchy to include additional Borel sets.
For example, every subset of Cantor or Baire space is a set ( that is, a set which equals the intersection of countably many open sets ).
Moreover, each of these open sets is and the list of Gödel numbers of these open sets has a computable enumeration.
If is a formula with a free set variable X and free number variables then the set is the intersection of the sets of the form as n ranges over the set of natural numbers.
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