The recursion theorem

In set theory, this is a theorem guaranteeing that recursively defined functions exist. Given a setX, an elementaofXand a function , the theorem states that there is a unique function (where denotes the set of natural numbers including zero) such that

for any natural numbern.

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Given a standard recitation of the "Recursion Theorem" is there a proper name for what is labeled the function "f" in the above statement, the f of f(F(n)).

If I were naming it I would call it the "Recursor function" as an analog of the "successor function" but as yet nobody has named me king. Is there is proper name for that function so that it can be talked about without the need to recite the Recursion theorem to make a specific reference.

That's it.