High Quality Content by WIKIPEDIA articles! In the mathematical discipline of set theory, 0# (zero sharp, also 0#) is the set of true formulas about (order)-indiscernibles in the Godel constructible universe. It is often encoded as a subset of the integers (using Godel numbering), or as a subset of the hereditarily finite sets, or (somewhat misleadingly) 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 formulas in Silver's 1966 thesis, later published as Silver (1971), where it was denoted by ?, and rediscovered by Solovay (1967), who considered it as a subset of the natural numbers and introduced the notation 0#.

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