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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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why do the Computability theory choose the natural number as the object of study? [closed]
I am wondering why the computable function is defined in the natural number set. Can people give me the answer or some resources that can solve my puzzle.