In mathematics, a hierarchy is a set-theoretical object, consisting of a preorder defined on a set. This is often referred to as an ordered set, though...

In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy (after mathematicians Stephen Cole Kleene and Andrzej...

as" one another. Hierarchy is an important concept in a wide variety of fields, such as architecture, philosophy, design, mathematics, computer science...

arithmetical hierarchy and analytical hierarchy from mathematical logic. The union of the classes in the hierarchy is denoted PH. Classes within the hierarchy have...

parent level. Hierarchies are typically depicted as a tree structures. Hierarchy may also refer to: Hierarchy (mathematics), the mathematical model of a...

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

In the theory of decision making, the analytic hierarchy process (AHP), also analytical hierarchy process, is a structured technique for organizing and...

Maslow's hierarchy of needs is a conceptualisation of the needs (or goals) that motivate human behaviour, which was proposed by the American psychologist...

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...

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

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...

In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets, denoted by V, is the class of hereditary...

In the mathematical field of descriptive set theory, a pointclass is a collection of sets of points, where a point is ordinarily understood to be an element...

theory, the exponential hierarchy is a hierarchy of complexity classes that is an exponential time analogue of the polynomial hierarchy. As elsewhere in complexity...

essentially all mathematical concepts can be modeled by pure sets. Sets in the von Neumann universe are organized into a cumulative hierarchy, based on how...

Containment hierarchy is used in class inheritance of object-oriented programming. Hereditarily countable set Hereditary property Hierarchy (mathematics) Nested...

effective Polish space. Borel hierarchy J. Steel, "What is... a Woodin cardinal?". Notices of the American Mathematical Society vol. 54, no. 9 (2007)...

proof theory, a fast-growing hierarchy (also called an extended Grzegorczyk hierarchy, or a Schwichtenberg-Wainer hierarchy) is an ordinal-indexed family...

boolean hierarchy is the hierarchy of boolean combinations (intersection, union and complementation) of NP sets. Equivalently, the boolean hierarchy can be...

attended the Gateway High School. Graham gained an interest in science and mathematics via his father who was a nuclear physicist. Graham received a Bachelor...

into a hierarchy based on their level of noncomputability? Although there is considerable overlap in terms of knowledge and methods, mathematical computability...

others. Abstract algebra Algebraic logic Abstract model theory Hierarchy (mathematics) Model theory Variety (universal algebra) Universal logic Font,...

In theoretical computer science and mathematics, the theory of computation is the branch that deals with what problems can be solved on a model of computation...

Peano Mathematical induction Structural induction Recursive definition Naive set theory Element (mathematics) Ur-element Singleton (mathematics) Simple...

In mathematics, specifically set theory, a cumulative hierarchy is a family of sets W α {\displaystyle W_{\alpha }} indexed by ordinals α {\displaystyle...

The Chomsky hierarchy in the fields of formal language theory, computer science, and linguistics, is a containment hierarchy of classes of formal grammars...

the broadest areas of mathematics, see Mathematics § Areas of mathematics. The Mathematics Subject Classification is a hierarchical list of areas and subjects...

In mathematics, the KdV hierarchy is an infinite sequence of partial differential equations which contains the Korteweg–de Vries equation. Let T {\displaystyle...

distributive property implies this as a natural hierarchy. As recently as the 1920s, the historian of mathematics Florian Cajori identifies disagreement about...

formulas is measured using the arithmetical hierarchy and analytical hierarchy. The reason that reverse mathematics is not carried out using set theory as...