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 natural numbers (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 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.
In the mathematical discipline of set theory, 0# (zerosharp, also 0#) is the set of true formulae about indiscernibles and order-indiscernibles in the...
Edward Sharpe and the Magnetic Zeros was an American folk rock band formed in Los Angeles, California, in 2005. The group was led by singer Alex Ebert...
investigated by Kurt Gödel, is inconsistent with the proposition that zerosharp exists and stronger large cardinal axioms (see list of large cardinal...
zero-sum, a theory in games and economics 0 sharp, also zerosharp or 0#, a concept in set theory 0 section, or zero section, a type of section in a Vector...
ZeroZeroZero is an Italian crime drama television series created by Stefano Sollima, Leonardo Fasoli and Mauricio Katz for Sky Atlantic, Canal+ and Amazon...
partial order 0# zerosharp, the set of true formulas about indiscernibles and order-indiscernibles in the constructible universe 0† zero dagger, a certain...
set theory) Tree (set theory) Union (set theory) Von Neumann universe Zerosharp Glossary of set theory List of large cardinal properties List of properties...
set theory) Tree (set theory) Union (set theory) Von Neumann universe Zerosharp Analytical hierarchy Almost Ramsey cardinal Erdős cardinal Extendible...
feature prominently in the theory of Ramsey cardinals, Erdős cardinals, and zerosharp. Identity of indiscernibles Rough set Jech, Thomas (2003). Set Theory...
under the assumption of the non-existence of zerosharp, establishing that L is the "core model below zerosharp". The work of Solovay isolated another core...
ISBN 978-1-903254-54-7. ０課の女 赤い手錠 (in Japanese). Movie Walker. Retrieved 2013-07-14. Sharp p. 328 "Zero WOMAN 警視庁０課の女(1995)" (in Japanese). AllCinema. Retrieved 2013-07-14...
flow occurs at the trailing edge and, because the radius of the sharp trailing edge is zero, the speed of the air around the trailing edge should be infinitely...
to zero, i.e., ϕ ( r ) ≥ 0 {\displaystyle \phi \ (r)\geq 0} . Therefore, when the limiter is equal to zero (sharp gradient, opposite slopes or zero gradient)...
The Mitsubishi A6M "Zero" is a long-range carrier-based fighter aircraft formerly manufactured by Mitsubishi Aircraft Company, a part of Mitsubishi Heavy...
from Sharp. The Sharp PC-1500, a BASIC-programmable pocket computer was released in 1981, followed by the improved Sharp PC-1600 in 1986 and the Sharp PC-E220...
Timm Sharp (born 1978) is an American actor and writer. He is known for his roles as Marshall Nesbitt in the Fox sitcom Undeclared, Doug Von Stuessen...
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