In computability theory a cylindric numbering is a special kind of numbering first introduced by Yuri L. Ershov in 1973.

If a numberings \nu is reducible to \mu then there exists a computable function f with \nu = \mu \circ f. Usually f is not injective but if \mu is a cylindric numbering we can always find an injective f.

Definition

A numbering \nu is called cylindric if

\nu \equiv_1 c(\nu).

That is if it is one-equivalent to its cylindrification

A set S is called cylindric if its indicator function

1_S: \mathbb{N} \to \{0,1\}

is a cylindric numbering.

Examples

• every Gödel numbering is cylindric

Properties

• cylindric numberings are idempotent, \nu \circ \nu = \nu

References

• Yu. L. Ershov, "Theorie der Numerierungen I." Zeitschrift für mathematische Logik und Grundlagen der Mathematik 19, 289-388 (1973).

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