Cylindric numbering
In computability theory a cylindric numbering is a special kind of numbering first introduced by Yuri L. Ershov in 1973.
If a numbering is reducible to then there exists a computable function with. Usually is not injective, but if is a cylindric numbering we can always find an injective.
Definition
A numbering is called cylindric ifThat is if it is one-equivalent to its cylindrification
A set is called cylindric if its indicator function
is a cylindric numbering.
Examples
- Every Gödel numbering is cylindric
Properties
- Cylindric numberings are idempotent: