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UBC CS TR-84-22 Summary

Recursion Theorems and Effective Domains, January 1984 K and Akira a

Every acceptable numbering of an effective domain is complete. Hence every effective domain admits the 2nd recursion theorem of Er\u{s}ov [1]. On the other hand for every effective domain, the 1st recursion theorem holds. In this note, we establish that for effective domains, the 2nd recursion theorem is strictly more general than the 1st recursion theorem, a generalization of an important result in recursive function theory.

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