Extensions
As is the case with the arithmetical hierarchy, a relativized version of the analytical hierarchy can be defined. The language is extended to add a constant set symbol A. A formula in the extended language is inductively defined to be or using the same inductive definition as above. Given a set, a set is defined to be if it is definable by a formula in which the symbol is interpreted as ; similar definitions for and apply. The sets that are or, for any parameter Y, are classified in the projective hierarchy.
Read more about this topic: Analytical Hierarchy
Famous quotes containing the word extensions:
“The psychological umbilical cord is more difficult to cut than the real one. We experience our children as extensions of ourselves, and we feel as though their behavior is an expression of something within us...instead of an expression of something in them. We see in our children our own reflection, and when we don’t like what we see, we feel angry at the reflection.”
—Elaine Heffner (20th century)
“If we focus exclusively on teaching our children to read, write, spell, and count in their first years of life, we turn our homes into extensions of school and turn bringing up a child into an exercise in curriculum development. We should be parents first and teachers of academic skills second.”
—Neil Kurshan (20th century)