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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
editA numbering is called cylindric if
That is if it is one-equivalent to its cylindrification
A set is called cylindric if its indicator function
is a cylindric numbering.
Examples
edit- Every Gödel numbering is cylindric
Properties
edit- Cylindric numberings are idempotent:
References
edit- Yu. L. Ershov, "Theorie der Numerierungen I." Zeitschrift für mathematische Logik und Grundlagen der Mathematik 19, 289-388 (1973).