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- W1010312920 abstract "Publisher Summary The successor function s(x) = xtl, where x is a variable ranging through the natural numbers, is a basic function in ordinary recursion theory. All the recursive functions can be generated from s and some other simple functions (projections and constant functions) by a few schemes. It is also chosen as a basic function in several settings of abstract recursion theory. In [31 Moschovakis defines the functions on an abstract domain by schemes, and is needed already to formulate the scheme of primitive recursion. For the same reason it is needed in the axiomatic approach in [41. [I] is also an axiomatic approach to recursion theory, and there Fenstad has proved some simple results from the axioms alone without using s (in chapter 1 , section 21, but s is brought in in the proofs of more advanced results, for instance the simple representation theorem 1.6.3: Let 0 be a precomputation theory. Then there exists a 0 - computable function f such that 0 is equivalent to PR[fl. Here PR[f] is a computation theory which is inductively defined by an operator r . The n-th level of r , denoted by rn, is defined from ,,n-l. The following result is an important part of the proof." @default.
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- W1010312920 date "1978-01-01" @default.
- W1010312920 modified "2023-09-24" @default.
- W1010312920 title "On The Role of the Successor Function in Recursion Theory" @default.
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