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- Mathematical logic hierarchies

Lévy hierarchy

In set theory and mathematical logic, the Lévy hierarchy, introduced by Azriel Lévy in 1965, is a hierarchy of formulas in the formal language of the Zermelo–Fraenkel set theory, which is typically ca

Borel hierarchy

In mathematical logic, the Borel hierarchy is a stratification of the Borel algebra generated by the open subsets of a Polish space; elements of this algebra are called Borel sets. Each Borel set is a

Difference hierarchy

In set theory, a branch of mathematics, the difference hierarchy over a pointclass is a hierarchy of larger pointclassesgenerated by taking differences of sets. If Γ is a pointclass, then the set of d

Arithmetical hierarchy

In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy (after mathematicians Stephen Cole Kleene and Andrzej Mostowski) classifies certain sets based on

Arithmetical set

In mathematical logic, an arithmetical set (or arithmetic set) is a set of natural numbers that can be defined by a formula of first-order Peano arithmetic. The arithmetical sets are classified by the

Analytical hierarchy

In mathematical logic and descriptive set theory, the analytical hierarchy is an extension of the arithmetical hierarchy. The analytical hierarchy of formulas includes formulas in the language of seco

Tarski–Kuratowski algorithm

In computability theory and mathematical logic the Tarski–Kuratowski algorithm is a non-deterministic algorithm which produces an upper bound for the complexity of a given formula in the arithmetical

Post's theorem

In computability theory Post's theorem, named after Emil Post, describes the connection between the arithmetical hierarchy and the Turing degrees.

Wadge hierarchy

In descriptive set theory, within mathematics, Wadge degrees are levels of complexity for sets of reals. Sets are compared by continuous reductions. The Wadge hierarchy is the structure of Wadge degre

Projective hierarchy

In the mathematical field of descriptive set theory, a subset of a Polish space is projective if it is for some positive integer . Here is
* if is analytic
* if the complement of , , is
* if there

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