In computability theory a cylindrification is a construction that associates a cylindric numbering to each numbering. The concept was first introduced by Yuri L. Ershov in 1973.
Definition
Given a numbering , the cylindrification is defined as
where is the Cantor pairing function.
Note that the cylindrification operation increases the input arity by 1.
Properties Given two numberings and then
References Yu. L. Ershov, "Theorie der Numerierungen I." Zeitschrift für mathematische Logik und Grundlagen der Mathematik 19, 289-388 (1973).