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Primitive recursive set function
In mathematics, primitive recursive set functions or primitive recursive ordinal functions are analogs of primitive recursive functions, defined for sets or ordinals rather than natural numbers. They were introduced by Jensen & Karp (1971).
A primitive recursive set function is a function from sets to sets that can be obtained from the following basic functions by repeatedly applying the following rules of substitution and recursion:
The basic functions are:
The rules for generating new functions by substitution are
where x and y are finite sequences of variables.
The rule for generating new functions by recursion is
A primitive recursive ordinal function is defined in the same way, except that the initial function F(x, y) = x ∪ {y} is replaced by F(x) = x ∪ {x} (the successor of x). The primitive recursive ordinal functions are the same as the primitive recursive set functions that map ordinals to ordinals.
Examples of primitive recursive set functions:
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Primitive recursive set function AI simulator
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Primitive recursive set function
In mathematics, primitive recursive set functions or primitive recursive ordinal functions are analogs of primitive recursive functions, defined for sets or ordinals rather than natural numbers. They were introduced by Jensen & Karp (1971).
A primitive recursive set function is a function from sets to sets that can be obtained from the following basic functions by repeatedly applying the following rules of substitution and recursion:
The basic functions are:
The rules for generating new functions by substitution are
where x and y are finite sequences of variables.
The rule for generating new functions by recursion is
A primitive recursive ordinal function is defined in the same way, except that the initial function F(x, y) = x ∪ {y} is replaced by F(x) = x ∪ {x} (the successor of x). The primitive recursive ordinal functions are the same as the primitive recursive set functions that map ordinals to ordinals.
Examples of primitive recursive set functions: