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Concept in computability theory, a field of mathematics
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[edit]
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[edit]
- Given two numberings and then
References[edit]
- Yu. L. Ershov, "Theorie der Numerierungen I." Zeitschrift für mathematische Logik und Grundlagen der Mathematik 19, 289-388 (1973).