In set theory, 0† (zero dagger) is a particular subset of the natural numbers, first defined by Robert M. Solovay in unpublished work in the 1960s. (The superscript † should be a dagger, but it appears as a plus sign on some browsers.) The definition is a bit awkward, because there might be no set of natural numbers satisfying the conditions. Specifically, if ZFC is consistent, then ZFC + "0† does not exist" is consistent. ZFC + "0† exists" is not known to be inconsistent (and most set theorists believe that it is consistent). In other words, it is believed to be independent (see large cardinal for a discussion). It is usually formulated as follows:
If 0† exists, then a careful analysis of the embeddings of L[U] into itself reveals that there is a closed unbounded subset of κ, and a closed unbounded proper class of ordinals greater than κ, which together are indiscernible for the structure , and 0† is defined to be the set of Gödel numbers of the true formulas about the indiscernibles in L[U].
When the night is falling
And the land is dark
Gentle it seems to be
Feel he's creeping and crawling
Feel he's creeping and crawling
No one turns on a light, be paralyzed
Be frozen tonight
No one turns on a light, be paralyzed
Be frozen tonight
Lost in the darkness, inevitable fate
Being haunted by a million screams
Feel he's creeping and crawling
Feel he's creeping and crawling
No one turns on a light, be paralyzed
Be frozen tonight
No one turns on a light, be paralyzed
Be frozen tonight
Deep tone violent sound
Faces hit onto the ground
When the fog comes over
As night becomes the day
Has swept it all away