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"... .51> zero(x) j 0 2. successor: defined by succ(x) j x + 1 3. projection: defined by proj n k (x 1 ; : : : ; xn ) j x k and two basic operators for constructing new functions: 1. composition: denoted by h k = comp( f n ; g k 1 ; g k 2 ; : : : ; g k n ) 2. primitive recursion: denoted ..."

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.51> zero(x) j 0 2. successor: defined by succ(x) j x + 1 3. projection: defined by proj n k (x 1 ; : : : ; xn ) j x k and two basic operators for constructing new functions: 1. composition: denoted by h k = comp( f n ; g k 1 ; g k 2 ; : : : ; g k n ) 2. primitive recursion: denoted by h n+1 = prec( f n ; g n+2 ) Here all arguments are natural numbers and the superscripts on the functions f , g, and h denote their "arities"; that is, the number of arg