About: Hyperarithmetical theory

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

About: Hyperarithmetical theory Goto Sponge NotDistinct Permalink

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

In recursion theory, hyperarithmetic theory is a generalization of Turing computability. It has close connections with definability in second-order arithmetic and with weak systems of set theory such as Kripke–Platek set theory. It is an important tool in effective descriptive set theory. The central focus of hyperarithmetic theory is the sets of natural numbers known as hyperarithmetic sets. There are three equivalent ways of defining this class of sets; the study of the relationships between these different definitions is one motivation for the study of hyperarithmetical theory.

Attributes	Values
rdfs:label	Hyperarithmetical theory (en)
rdfs:comment	In recursion theory, hyperarithmetic theory is a generalization of Turing computability. It has close connections with definability in second-order arithmetic and with weak systems of set theory such as Kripke–Platek set theory. It is an important tool in effective descriptive set theory. The central focus of hyperarithmetic theory is the sets of natural numbers known as hyperarithmetic sets. There are three equivalent ways of defining this class of sets; the study of the relationships between these different definitions is one motivation for the study of hyperarithmetical theory. (en)
sameAs	Hyperarithmetical theory
dbp:wikiPageUsesTemplate	dbt:ISBN dbt:Pointclasses
Subject	Computability theory Hierarchy
gold:hypernym	Generalization
prov:wasDerivedFrom	http://en.wikipedia.org/wiki/Hyperarithmetical_theory?oldid=1046769618&ns=0
Wikipage page ID	12383591 (xsd:integer)
page length (characters) of wiki page	12500 (xsd:nonNegativeInteger)
Wikipage revision ID	1046769618 (xsd:integer)
Link from a Wikipage to another Wikipage	Admissible ordinal Analytical hierarchy Arithmetical hierarchy Arithmetical set Baire space Tarski's undefinability theorem Turing degree Turing jump Turing reduction Computability theory Julia F. Knight Hierarchy Pairing function Second-order arithmetic Set theory Computability theory Computable function Computable ordinal Effective descriptive set theory Ordinal notation Ordinal number Infimum and supremum Kripke–Platek set theory Many-one reduction Peano axioms Type theory Large countable ordinal Limit ordinal History of numbers Alpha recursion theory
has abstract	In recursion theory, hyperarithmetic theory is a generalization of Turing computability. It has close connections with definability in second-order arithmetic and with weak systems of set theory such as Kripke–Platek set theory. It is an important tool in effective descriptive set theory. The central focus of hyperarithmetic theory is the sets of natural numbers known as hyperarithmetic sets. There are three equivalent ways of defining this class of sets; the study of the relationships between these different definitions is one motivation for the study of hyperarithmetical theory. (en)
foaf:isPrimaryTopicOf	http://en.wikipedia.org/wiki/Hyperarithmetical_theory
is Wikipage redirect of	Hyperarithmetic theory Hyperarithmetic Hyperarithmetic hierarchy Hyperarithmetic reducibility Hyperarithmetic set Hyperarithmetical Hyperarithmetical hierarchy Hyperarithmetical reducibility Hyperarithmetical set Hyperjump
is Link from a Wikipage to another Wikipage of	List of types of sets Nonrecursive ordinal Analytical hierarchy Arithmetical hierarchy Basis theorem (computability) Borel hierarchy Glossary of set theory Kai Wehmeier Hyperarithmetic theory Hypercomputation Computability theory Computable function Computable number Constructible universe Hierarchy (mathematics) Hilary Putnam Descriptive set theory Mathematical logic Hyperarithmetic Hyperarithmetic hierarchy Hyperarithmetic reducibility Hyperarithmetic set Hyperarithmetical Hyperarithmetical hierarchy Hyperarithmetical reducibility Hyperarithmetical set Hyperjump
is foaf:primaryTopic of	http://en.wikipedia.org/wiki/Hyperarithmetical_theory

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