"Projective set" redirects here. For the card game, see Projective Set (game).
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 is a Polish space and a subset such that is the projection of onto ; that is,
The choice of the Polish space in the third clause above is not very important; it could be replaced in the definition by a fixed uncountable Polish space, say Baire space or Cantor space or the real line.
and 24 Related for: Projective hierarchy information
is projective iff it is definable in the language of second-order arithmetic from some real parameter. A similar relationship between the projective hierarchy...
analytical hierarchy of sets classifies sets by the formulas that can be used to define them; it is the lightface version of the projectivehierarchy. The notation...
phenomenon is particularly apparent in the projective sets. These are defined via the projectivehierarchy on a Polish space X: A set is declared to be...
called Σ 1 1 {\displaystyle {\boldsymbol {\Sigma }}_{1}^{1}} (see projectivehierarchy). Note that the bold font in this symbol is not the Wikipedia convention...
variety Projective linear group Projective module Projective line Projective object Projective transformation ProjectivehierarchyProjective connection...
spaces themselves). The pointclasses in the Borel hierarchy, and in the more complex projectivehierarchy, are represented by sub- and super-scripted Greek...
In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy or Kleene–Mostowski hierarchy (after mathematicians Stephen Cole Kleene and Andrzej...
cardinals, then projective determinacy holds; that is, every game whose winning condition is a projective set is determined. From projective determinacy it...
pointclasses in the Borel hierarchy and extends to the study of more complex hierarchies such as the projectivehierarchy and the Wadge hierarchy. Many properties...
in L(R) and that a game is determined if it has a projective set as its winning set (see Projective determinacy). The axiom of determinacy implies that...
as Π 1 1 {\displaystyle {\boldsymbol {\Pi }}_{1}^{1}} sets (see projectivehierarchy). Kechris, Alexander S. (1994), Classical Descriptive Set Theory...
In the theory of decision making, the analytic hierarchy process (AHP), also analytical hierarchy process, is a structured technique for organizing and...
The hierarchy of the Catholic Church consists of its bishops, priests, and deacons. In the ecclesiological sense of the term, "hierarchy" strictly means...
In set theory, a branch of mathematics, the difference hierarchy over a pointclass is a hierarchy of larger pointclasses generated by taking differences...
example projective geometry rightly talked about conic sections, but not about circles or angles because those notions were not invariant under projective transformations...
sets of reals. Sets are compared by continuous reductions. The Wadge hierarchy is the structure of Wadge degrees. These concepts are named after William...
Data hierarchy refers to the systematic organization of data, often in a hierarchical form. Data organization involves characters, fields, records, files...
Hierarchy of hazard control is a system used in industry to prioritize possible interventions to minimize or eliminate exposure to hazards. It is a widely...
In computer science, the method of contraction hierarchies is a speed-up technique for finding the shortest-path in a graph. The most intuitive applications...
The street hierarchy is an urban planning technique for laying out road networks that exclude automobile through-traffic from developed areas. It is conceived...
structure as a "hierarchical decomposition of the total scope of work to be carried out by the project team to accomplish the project objectives and create...
have a similar hierarchy: Absolutive > Ergative > Indirect Object > etc. (same as above) This order is called the accessibility hierarchy. If a language...
projective 1. A projective set is a set that can be obtained from an analytic set by repeatedly taking complements and projections 2. Projective determinacy...
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