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Members of <math>L_\alpha</math> are called <math>\alpha</math> finite and play a similar role to the finite numbers in classical recursion theory.
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.
''A'' is said to be α-recusive in ''B'' if there exist <math>R_0,R_1</math> reduction procedures such that:
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