Cylindric numbering

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

Properties

References