Alternative Characterization
For subsets of Baire space or Cantor space, there is a more concise (if less transparent) alternative definition, which turns out to be equivalent. A subset A of Baire space is ∞-Borel just in case there is a set of ordinals S and a first-order formula φ of the language of set theory such that, for every x in Baire space,
where L is Gödel's constructible universe relativized to S and x. When using this definition, the ∞-Borel code is made up of the set S and the formula φ, taken together.
Read more about this topic: Infinity-Borel Set
Famous quotes containing the word alternative:
“If English is spoken in heaven ... God undoubtedly employs Cranmer as his speechwriter. The angels of the lesser ministries probably use the language of the New English Bible and the Alternative Service Book for internal memos.”
—Charles, Prince Of Wales (b. 1948)