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- Zero_sharp 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 Silver (1971), where it was denoted by Σ, and rediscovered by Solovay (1967, 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 a number 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.".
- Zero_sharp wikiPageExternalLink tresc.php?wyd=1&tom=66.
- Zero_sharp wikiPageID "248085".
- Zero_sharp wikiPageLength "8424".
- Zero_sharp wikiPageOutDegree "46".
- Zero_sharp wikiPageRevisionID "674929853".
- Zero_sharp wikiPageWikiLink Axiom_of_constructibility.
- Zero_sharp wikiPageWikiLink Axiomatic_set_theory.
- Zero_sharp wikiPageWikiLink Baire_space_(set_theory).
- Zero_sharp wikiPageWikiLink Cardinal_number.
- Zero_sharp wikiPageWikiLink Cardinality.
- Zero_sharp wikiPageWikiLink Category:Constructible_universe.
- Zero_sharp wikiPageWikiLink Category:Determinacy.
- Zero_sharp wikiPageWikiLink Category:Large_cardinals.
- Zero_sharp wikiPageWikiLink Category:Real_numbers.
- Zero_sharp wikiPageWikiLink Changs_conjecture.
- Zero_sharp wikiPageWikiLink Cofinal_(mathematics).
- Zero_sharp wikiPageWikiLink Cofinality.
- Zero_sharp wikiPageWikiLink Constructible_universe.
- Zero_sharp wikiPageWikiLink Donald_A._Martin.
- Zero_sharp wikiPageWikiLink Erdős_cardinal.
- Zero_sharp wikiPageWikiLink Forcing_(mathematics).
- Zero_sharp wikiPageWikiLink Formula_(mathematical_logic).
- Zero_sharp wikiPageWikiLink Generic_filter.
- Zero_sharp wikiPageWikiLink Gödel_constructible_universe.
- Zero_sharp wikiPageWikiLink Gödel_number.
- Zero_sharp wikiPageWikiLink Gödel_numbering.
- Zero_sharp wikiPageWikiLink Hereditarily_finite_set.
- Zero_sharp wikiPageWikiLink Indiscernibles.
- Zero_sharp wikiPageWikiLink Ineffable_cardinal.
- Zero_sharp wikiPageWikiLink Jack_Silver.
- Zero_sharp wikiPageWikiLink Jensens_covering_lemma.
- Zero_sharp wikiPageWikiLink Jensens_covering_theorem.
- Zero_sharp wikiPageWikiLink Large_cardinal.
- Zero_sharp wikiPageWikiLink Leo_Harrington.
- Zero_sharp wikiPageWikiLink Lightface_analytic_game.
- Zero_sharp wikiPageWikiLink List_of_forcing_notions.
- Zero_sharp wikiPageWikiLink Measurable_cardinal.
- Zero_sharp wikiPageWikiLink Ramsey_cardinal.
- Zero_sharp wikiPageWikiLink Regular_cardinal.
- Zero_sharp wikiPageWikiLink Ronald_Jensen.
- Zero_sharp wikiPageWikiLink Set_theory.
- Zero_sharp wikiPageWikiLink Springer-Verlag.
- Zero_sharp wikiPageWikiLink Springer_Science+Business_Media.
- Zero_sharp wikiPageWikiLink Tarskis_undefinability_theorem.
- Zero_sharp wikiPageWikiLink Transactions_of_the_American_Mathematical_Society.
- Zero_sharp wikiPageWikiLink Turing_degree.
- Zero_sharp wikiPageWikiLink Uncountable_set.
- Zero_sharp wikiPageWikiLink Well-formed_formula.
- Zero_sharp wikiPageWikiLink ZFC.
- Zero_sharp wikiPageWikiLink Zermelo–Fraenkel_set_theory.
- Zero_sharp wikiPageWikiLink Zero_dagger.
- Zero_sharp wikiPageWikiLinkText "0#".
- Zero_sharp wikiPageWikiLinkText "Zero sharp".
- Zero_sharp wikiPageWikiLinkText "Zero_sharp".
- Zero_sharp wikiPageWikiLinkText "zero sharp".
- Zero_sharp b "2".
- Zero_sharp b "3".
- Zero_sharp hasPhotoCollection Zero_sharp.
- Zero_sharp p "1".
- Zero_sharp wikiPageUsesTemplate Template:Citation.
- Zero_sharp wikiPageUsesTemplate Template:Cite_book.
- Zero_sharp wikiPageUsesTemplate Template:Harvtxt.
- Zero_sharp wikiPageUsesTemplate Template:Su.
- Zero_sharp subject Category:Constructible_universe.
- Zero_sharp subject Category:Determinacy.
- Zero_sharp subject Category:Large_cardinals.
- Zero_sharp subject Category:Real_numbers.
- Zero_sharp hypernym Set.
- Zero_sharp 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.".
- Zero_sharp label "Zero sharp".
- Zero_sharp sameAs m.01kwj8.
- Zero_sharp sameAs Q8069610.
- Zero_sharp sameAs Q8069610.
- Zero_sharp wasDerivedFrom Zero_sharp?oldid=674929853.
- Zero_sharp isPrimaryTopicOf Zero_sharp.