About: Analytical hierarchy

Facets (new session)
Description
Metadata
Settings
- Rule:
- Inverse Functional Properties:
- "Same As":

About: Analytical hierarchy Goto Sponge NotDistinct Permalink

An Entity of Type : owl:Thing, within Data Space : el.dbpedia.org associated with source document(s)

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 second-order arithmetic, which can have quantifiers over both the set of natural numbers, , and over functions from to . The analytical hierarchy of sets classifies sets by the formulas that can be used to define them; it is the lightface version of the projective hierarchy.

Attributes	Values
rdfs:label	Analytical hierarchy (en)
rdfs:comment	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 second-order arithmetic, which can have quantifiers over both the set of natural numbers, , and over functions from to . The analytical hierarchy of sets classifies sets by the formulas that can be used to define them; it is the lightface version of the projective hierarchy. (en)
sameAs	Analytical hierarchy Analytical hierarchy
dbp:wikiPageUsesTemplate	dbt:Cite_book dbt:Otheruses4 dbt:Planetmath dbt:Pointclasses
Subject	Computability theory Hierarchy Effective descriptive set theory Mathematical logic hierarchies
Link from a Wikipage to an external page	https://archive.org/details/classicaldescrip0000kech https://archive.org/details/theoryofrecursiv00roge
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Analytical_hierarchy?oldid=1053586628&ns=0
Wikipage page ID	634233 (xsd:integer)
page length (characters) of wiki page	8375 (xsd:nonNegativeInteger)
Wikipage revision ID	1053586628 (xsd:integer)
Link from a Wikipage to another Wikipage	Logical equivalence Projective hierarchy Well-order Analytic set Arithmetical hierarchy Axiom of constructibility Baire space (set theory) Cantor space Computability theory Hierarchy Second-order arithmetic Hyperarithmetical theory Prenex normal form Effective Polish space Effective descriptive set theory Mathematical logic hierarchies Descriptive set theory Fast-growing hierarchy Mathematical logic History of numbers Pointclass Polish space Real number Alpha recursion theory
has abstract	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 second-order arithmetic, which can have quantifiers over both the set of natural numbers, , and over functions from to . The analytical hierarchy of sets classifies sets by the formulas that can be used to define them; it is the lightface version of the projective hierarchy. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Analytical_hierarchy
is differentFrom of	Analytic set
is Wikipage redirect of	Analytic hierarchy Analytical set
is Link from a Wikipage to another Wikipage of	List of types of sets Absoluteness Analytic Analytic set Arithmetical hierarchy Axiom of constructibility Basis theorem (computability) Borel hierarchy George Boolos Glossary of set theory Definable real number Definable set Delta Hyperarithmetical theory List of mathematical logic topics List of set theory topics Computability theory Conservative extension Hierarchy (mathematics) Hilary Putnam List of algorithms Independence-friendly logic Index of philosophy articles (A–C) Descriptive set theory Fast-growing hierarchy Kőnig's lemma Kleene's O Analytic hierarchy Analytical set
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Analytical_hierarchy

Faceted Search & Find service v1.17_git151 as of Feb 20 2025

Alternative Linked Data Documents: ODE Content Formats:

RDF

ODATA

Microdata

About

OpenLink Virtuoso version 07.20.3240 as of Nov 11 2024, on Linux (x86_64-ubuntu_focal-linux-gnu), Single-Server Edition (72 GB total memory, 1 GB memory in use)
Data on this page belongs to its respective rights holders.
Virtuoso Faceted Browser Copyright © 2009-2025 OpenLink Software