View source for Enumeration problem

An [[Algorithmic problem|algorithmic problem]] in which one has to construct an algorithm that enumerates <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035820/e0358201.png" /> for a given set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035820/e0358202.png" />, i.e. an algorithm <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035820/e0358203.png" /> that is applicable to any natural number, that converts it to an element of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035820/e0358204.png" /> and such that any element of <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035820/e0358205.png" /> is obtained by applying <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035820/e0358206.png" /> to some natural number; in other words, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035820/e0358207.png" />. The enumeration problem for a set <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035820/e0358208.png" /> is solvable (i.e. such an <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035820/e0358209.png" /> exists) if and only if <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/e/e035/e035820/e03582010.png" /> is a non-empty [[Enumerable set|enumerable set]].