A second difference is that the first recursion theorem only applies to systems of equations that can be recast as recursive operators.
12.
The proof of part 1 of the first recursion theorem is obtained by iterating the enumeration operator & Phi; beginning with the empty set.
13.
By the corollary to the recursion theorem, there is an index e such that \ phi _ e ( y ) returns Q ( e, y ).
14.
A number of mathematical concepts are named after him : Kleene hierarchy, Kleene algebra, the Kleene star ( Kleene closure ), Kleene's recursion theorem and the Kleene fixpoint theorem.
15.
Rogers [ 1967 ] uses the term "'weak recursion theorem "'for the first recursion theorem and "'strong recursion theorem "'for the second recursion theorem.
16.
Rogers [ 1967 ] uses the term "'weak recursion theorem "'for the first recursion theorem and "'strong recursion theorem "'for the second recursion theorem.
17.
Rogers [ 1967 ] uses the term "'weak recursion theorem "'for the first recursion theorem and "'strong recursion theorem "'for the second recursion theorem.
18.
Rogers [ 1967 ] uses the term "'weak recursion theorem "'for the first recursion theorem and "'strong recursion theorem "'for the second recursion theorem.
19.
One difference between the first and second recursion theorems is that the fixed points obtained by the first recursion theorem are guaranteed to be least fixed points, while those obtained from the second recursion theorem may not be least fixed points.
20.
One difference between the first and second recursion theorems is that the fixed points obtained by the first recursion theorem are guaranteed to be least fixed points, while those obtained from the second recursion theorem may not be least fixed points.
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