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Additional connections between recursion theory and α recursion theory can be drawn, although explicit definitions may not have yet been written to formalize them:
*The functions <math>\Delta_0</math>-definable in <math>(L_\alpha,\in)</math> play a role similar to those of the [[Primitive recursion|primitive recursive functions]].<ref name="relconstr" />
We say R is a reduction procedure if it is <math>\alpha</math> recursively enumerable and every member of R is of the form <math> \langle H,J,K \rangle </math> where ''H'', ''J'', ''K'' are all α-finite.
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