Independence Results for n-Ary Recursion Theorems

The n-ary first and second recursion theorems formalize two distinct, yet similar, notions of self-reference. Roughly, the n-ary first recursion theorem says that, for any n algorithmic tasks (of an appropriate type), there exist n partial computable functions that use their own graphs in the manner prescribed by those tasks; the n-ary second recursion theorem says that, for any n algorithmic tasks (of an appropriate type), there exist n programs that use their own source code in the manner prescribed by those tasks. Results include the following. The constructive 1-ary form of the first recursion theorem is independent of either 1-ary form of the second recursion theorem. The constructive 1-ary form of the first recursion theorem does not imply the constructive 2-ary form; however, the constructive

• Type: Conference
• Year: 2009
• Where: FCT
• Authors: John Case, Samuel E. Moelius
• Keywords: FCT 2009, N-ary first Recursion, Recursion Theorem, Theoretical Computer Science, first Recursion Theorem