The Analytical Hierarchy of Sets of Natural Numbers
A set of natural numbers is assigned the classification if it is definable by a formula. The set is assigned the classification if it is definable by a formula. If the set is both and then it is given the additional classification .
The sets are called hyperarithmetical. An alternate classification of these sets by way of iterated computable functionals is provided by hyperarithmetical theory.
Read more about this topic: Analytical Hierarchy
Famous quotes containing the words analytical, hierarchy, sets, natural and/or numbers:
“I have seen too much not to know that the impression of a woman may be more valuable than the conclusion of an analytical reasoner.”
—Sir Arthur Conan Doyle (1859–1930)
“In a hierarchy every employee tends to rise to his level of incompetence.”
—Laurence J. Peter (1919–1990)
“This is certainly not the place for a discourse about what festivals are for. Discussions on this theme were plentiful during that phase of preparation and on the whole were fruitless. My experience is that discussion is fruitless. What sets forth and demonstrates is the sight of events in action, is living through these events and understanding them.”
—Doris Lessing (b. 1919)
“She had been forced into prudence in her youth, she learned romance as she grew older—the natural sequel of an unnatural beginning.”
—Jane Austen (1775–1817)
“And when all bodies meet
In Lethe to be drowned,
Then only numbers sweet
With endless life are crowned.”
—Robert Herrick (1591–1674)