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 S, and rediscovered by , 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).