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)
“We love the indomitable bellicose patriotism that sets you apart; we love the national pride that guides your muscularly courageous race; we love the potent individualism that doesn’t prevent you from opening your arms to individualists of every land, whether libertarians or anarchists.”
—Tommaso Marinetti (1876–1944)
“The Reverend Samuel Peters ... exaggerated the Blue Laws, but they did include “Capital Lawes” providing a death penalty for any child over sixteen who was found guilty of cursing or striking his natural parents; a death penalty for an incorrigible son; a law forbidding smoking except in a room in a private house; another law declaring smoking illegal except on a journey five miles away from home,...”
—Administration for the State of Con, U.S. public relief program (1935-1943)
“Old age equalizes—we are aware that what is happening to us has happened to untold numbers from the beginning of time. When we are young we act as if we were the first young people in the world.”
—Eric Hoffer (1902–1983)