Alpha recursion theory: Difference between revisions

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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-recusiverecursive in ''B'' if there exist <math>R_0,R_1</math> reduction procedures such that:

: <math>K \subseteq A \leftrightarrow \exists H: \exists J:[\langle H,J,K \rangle \in R_0 \wedge H \subseteq B \wedge J \subseteq \alpha / B ],</math>