However, Kleene's , when taken as a whole, is (see analytical hierarchy).

The low basis theorem in computability theory states that every nonempty class in (see analytical hierarchy) contains a set of low degree.

It is a resource-bounded counterpart to the arithmetical hierarchy and analytical hierarchy from mathematical logic.

The concept is essential for developing the arithmetical hierarchy and the analytical hierarchy.

The first definition of the hyperarithmetic sets uses the analytical hierarchy.

Its lightface analog is known as the analytical hierarchy.

(See analytical hierarchy for the analogous construction of second-order arithmetic.)

In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy.

As is the case with the arithmetical hierarchy, a relativized version of the analytical hierarchy can be defined.

In this context, the complexity of formulas is measured using the arithmetical hierarchy and analytical hierarchy.