hierarchy of sets

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• Hierarchy — A hierarchy (Greek: hierarchia (ἱεραρχία), from hierarches, leader of sacred rites ) is an arrangement of items (objects, names, values, categories, etc.) in which the items are represented as being above, below, or at the same level as one… …   Wikipedia

• Hierarchy of precious substances — In popular culture, sets of precious substances may form hierarchies which express conventional perceived relative value or merit. Precious metals appear prominently in such hierarchies, but as they grow, gems and semi precious materials may be… …   Wikipedia

• Arithmetical hierarchy — In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene hierarchy classifies certain sets based on the complexity of formulas that define them. Any set that receives a classification is called arithmetical. The… …   Wikipedia

• 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 assigned a unique countable ordinal number… …   Wikipedia

• Analytical hierarchy — In mathematical logic and descriptive set theory, the analytical hierarchy is a higher type analogue of the arithmetical hierarchy. It thus continues the classification of sets by the formulas that define them. The analytical hierarchy of… …   Wikipedia

• Grzegorczyk hierarchy — The Grzegorczyk hierarchy, named after the Polish logician Andrzej Grzegorczyk, is a hierarchy of sets of functions used in recursive function theory. Every function in the Grzegorczyk hierarchy is a primitive recursive function, and every… …   Wikipedia

• Wadge hierarchy — In descriptive set theory, Wadge degrees are levels of complexity for sets of reals and more comprehensively, subsets of any given topological space. Sets are compared by continuous reductions. The Wadge hierarchy is the structure of Wadge… …   Wikipedia

• Projective hierarchy — In the mathematical field of descriptive set theory, a subset A of a Polish space X is projective if it is oldsymbol{Sigma}^1 n for some positive integer n. Here A is * oldsymbol{Sigma}^1 1 if A is analytic * oldsymbol{Pi}^1 n if the… …   Wikipedia

• Recursive languages and sets — This article is a temporary experiment to see whether it is feasible and desirable to merge the articles Recursive set, Recursive language, Decidable language, Decidable problem and Undecidable problem. Input on how best to do this is very much… …   Wikipedia

• Spiritual Hierarchy — Part of a series on Theosophy Founders of the T. S. Helena Blavatsky · …   Wikipedia

• Difference hierarchy — In set theory, the difference hierarchy over a pointclass is a hierarchy of larger pointclasses generated by taking differences of sets. If Γ is a pointclass, then the set of differences in Γ is . In usual notation, this set is denoted by 2 Γ.… …   Wikipedia