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)
“The poem has a social effect of some kind whether or not the poet wills it to have. It has kinetic force, it sets in motion ... [ellipsis in source] elements in the reader that would otherwise be stagnant.”
—Denise Levertov (b. 1923)
“All is changed. All looks strange to me and gives me a feeling which I would rather get away from, although I know it to be the carrying out of natural laws. And I am not complaining. I am doing the same as many old people have done, I suppose, who have led an active life and suddenly find themselves living without a purpose. Oh, my heart is so full. I could write a big book on the subject of going out of this world gracefully.”
—Maria D. Brown (1827–1927)
“I’m not even thinking straight any more. Numbers buzz in my head like wasps.”
—Kurt Neumann (1906–1958)