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:
“A mental disease has swept the planet: banalization.... Presented with the alternative of love or a garbage disposal unit, young people of all countries have chosen the garbage disposal unit.”
—Ivan Chtcheglov (b. 1934)