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)
“To the extent to which genius can be conjoined with a merely good human being, Haydn possessed genius. He never exceeds the limits that morality sets for the intellect; he only composes music which has “no past.””
—Friedrich Nietzsche (1844–1900)
“The very natural tendency to use terms derived from traditional grammar like verb, noun, adjective, passive voice, in describing languages outside of Indo-European is fraught with grave possibilities of misunderstanding.”
—Benjamin Lee Whorf (1897–1934)
“I had a feeling that out there, there were very poor people who didn’t have enough to eat. But they wore wonderfully colored rags and did musical numbers up and down the streets together.”
—Jill Robinson (b. 1936)