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computable sets and functions, Turing degrees, c.e. degrees, models of computability, primitive recursion, oracle computation, models of computability, decision problems, undecidability, Turing jump, halting problem, notions of computable randomness, computable model theory, computable equivalence relation theory, arithmetic and hyperarithmetic hierarchy, infinitary computability, $\alpha$-recursion, complexity theory.
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A question on s-m-n Theorem
Let $\phi$ be an acceptable programming system. If $f(x,y)$ is a $2$-ary partial recursive function, by the s-m-n Theorem there exists a $1$-ary recursive function $r$ such that, for all $x$ and $y$, …