User blog comment:Nayuta Ito/What We've Agreed on Stage Cardinal/@comment-11227630-20180522030604/@comment-2001:56A:71A8:5F00:C801:4C6D:105A:CD53-20180525032605

Hyp cos, that's wrong:

In your version, S(T^2) is equivalent to I(1,0), so the psi_S(T^2) function enumerates the fixed points of a -> S(T*a). Which is fine.

But if S(T^T) = M, then the psi_S(T^T) function is MUCH MORE POWERFUL than just giving fixed points of a -> S(T^a). That is a problem. If psi_S(T^T) just gave fixed points, then S(T^T) would be equivalent to I(1,0,0), and S(e(T+1)) would just be X(e(M+1)) which obviously isn't powerful enough. So how do you know when a function is taking fixed points and when it isn't? Why does S(T^2) do that, but not S(T^T)?

Also, on a related note, how would you express I(1,0,0) or I(1,0,0,0) in your S function?

(btw this is ecl1)