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)
““Having reached the term of his natural life”; Mwould it not be truer to say, Having reached the term of his unnatural life?”
—Henry David Thoreau (1817–1862)
“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)