Cylindrification
From Wikipedia, the free encyclopedia
In computability theory a cylindrification is a construction which associates a cylindric numbering to each numbering. The concept was first introduced by Yuri L. Ershov in 1973.
[edit] Definition
Given a numbering ν the cyclindrification c(ν) is defined as
where 
is the Cantor pairing function. The cylindrification operation takes a relation as input of arity k and outputs a relation of arity k + 1 as follows : Given a relaton R of arity K, its cylindrification denoted by c(R), is the following set {(a1,...,ak,a)|(a1,...,ak)belongs to R and a belongs to A}. Note that the cylindrification operation increases the arity of an input by 1.
[edit] Properties
- Given two numberings ν and μ then
[edit] References
- Yu. L. Ershov, "Theorie der Numerierungen I." Zeitschrift für mathematische Logik und Grundlagen der Mathematik 19, 289-388 (1973).
