User blog comment:Kyodaisuu/English description of Fish numbers/@comment-25418284-20131102173245

I'm not convinced by the extension. A function f can be defined as a set of ordered pairs (a, b), where no two pairs have the same first element. It is not hard to define function calls f(n) and test for equality as in f(a)=b. In fact, I have already done so. The oracle that you've tried to create is, unfortunately, already embedded in Rayo's function :(