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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').

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rdfs:label	Zero sharp (en)
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)
dcterms:subject	Real numbers Determinacy Constructible universe Large cardinals
Wikipage page ID	248085 (xsd:integer)
Wikipage revision ID	1117468071 (xsd:integer)
Link from a Wikipage to another Wikipage	Robert M. Solovay Ronald Jensen List of forcing notions Donald A. Martin Indiscernibles Lightface analytic game Real numbers Constructible universe Measurable cardinal Generic filter Erdős cardinal Leo Harrington Axiomatic set theory Gödel numbering Large cardinal Forcing (mathematics) Cardinal number Cardinality Regular cardinal Jack Silver Baire space (set theory) Jensen's covering theorem Determinacy Cofinal (mathematics) Cofinality Hereditarily finite set ZFC Zero dagger Axiom of constructibility Constructible universe Large cardinals Ineffable cardinal Chang's conjecture Set theory Ramsey cardinal Tarski's undefinability theorem Turing degree Uncountable set Transactions of the American Mathematical Society Springer-Verlag Jensen's covering lemma Formula (mathematical logic) Gödel constructible universe Gödel number
Link from a Wikipage to an external page	http://matwbn.icm.edu.pl/tresc.php%3Fwyd=1&tom=66
sameAs	Zero sharp Zero sharp Zero sharp Zero sharp
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has 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)
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foaf:isPrimaryTopicOf	wikipedia-en:Zero_sharp
is Link from a Wikipage to another Wikipage of	Robert M. Solovay Determinacy Indiscernibles Lightface analytic game List of large cardinal properties List of mathematical logic topics List of set theory topics 0S 0 (disambiguation) Constructible universe Menachem Magidor Zero (disambiguation) Glossary of set theory Core model

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