About: Zero sharp

An Entity of Type: Person100007846, from Named Graph: http://dbpedia.org, within Data Space: dbpedia.org

In the mathematical discipline of set theory, 0# (zero sharp, also 0#) is the set of true formulae about indiscernibles and order-indiscernibles in the Gödel constructible universe. It is often encoded as a subset of the integers (using Gödel numbering), or as a subset of the hereditarily finite sets, or as a real number. Its existence is unprovable in ZFC, the standard form of axiomatic set theory, but follows from a suitable large cardinal axiom. It was first introduced as a set of formulae in Silver's 1966 thesis, later published as , where it was denoted by Σ, and rediscovered by , p.52), who considered it as a subset of the natural numbers and introduced the notation O# (with a capital letter O; this later changed to the numeral '0').

Property Value
dbo:abstract
  • In the mathematical discipline of set theory, 0# (zero sharp, also 0#) is the set of true formulae about indiscernibles and order-indiscernibles in the Gödel constructible universe. It is often encoded as a subset of the integers (using Gödel numbering), or as a subset of the hereditarily finite sets, or as a real number. Its existence is unprovable in ZFC, the standard form of axiomatic set theory, but follows from a suitable large cardinal axiom. It was first introduced as a set of formulae in Silver's 1966 thesis, later published as , where it was denoted by Σ, and rediscovered by , p.52), who considered it as a subset of the natural numbers and introduced the notation O# (with a capital letter O; this later changed to the numeral '0'). Roughly speaking, if 0# exists then the universe V of sets is much larger than the universe L of constructible sets, while if it does not exist then the universe of all sets is closely approximated by the constructible sets. (en)
dbo:wikiPageExternalLink
dbo:wikiPageID
  • 248085 (xsd:integer)
dbo:wikiPageLength
  • 9046 (xsd:nonNegativeInteger)
dbo:wikiPageRevisionID
  • 1117468071 (xsd:integer)
dbo:wikiPageWikiLink
dbp:b
  • 2 (xsd:integer)
  • 3 (xsd:integer)
dbp:p
  • 1 (xsd:integer)
dbp:wikiPageUsesTemplate
dcterms:subject
gold:hypernym
rdf:type
rdfs:comment
  • In the mathematical discipline of set theory, 0# (zero sharp, also 0#) is the set of true formulae about indiscernibles and order-indiscernibles in the Gödel constructible universe. It is often encoded as a subset of the integers (using Gödel numbering), or as a subset of the hereditarily finite sets, or as a real number. Its existence is unprovable in ZFC, the standard form of axiomatic set theory, but follows from a suitable large cardinal axiom. It was first introduced as a set of formulae in Silver's 1966 thesis, later published as , where it was denoted by Σ, and rediscovered by , p.52), who considered it as a subset of the natural numbers and introduced the notation O# (with a capital letter O; this later changed to the numeral '0'). (en)
rdfs:label
  • Zero sharp (en)
owl:sameAs
prov:wasDerivedFrom
foaf:isPrimaryTopicOf
is dbo:knownFor of
is dbo:wikiPageDisambiguates of
is dbo:wikiPageRedirects of
is dbo:wikiPageWikiLink of
is dbp:knownFor of
is foaf:primaryTopic of
Powered by OpenLink Virtuoso    This material is Open Knowledge     W3C Semantic Web Technology     This material is Open Knowledge    Valid XHTML + RDFa
This content was extracted from Wikipedia and is licensed under the Creative Commons Attribution-ShareAlike 3.0 Unported License