User blog comment:PsiCubed2/How to make Deedlit's Mahlo-level notation more intuitive/@comment-35470197-20180807000338/@comment-30754445-20180807014547

My I(M2) = Deedlit's I(1,0,0)

I'm not sure how anyone could be confused this, 'considering that Deedlit gave pretty much the exact same relations in his own blog post. '

I'm even more baffled by your request that I define I(α), when my entire suggestion is a single line that defines exactly that: I(M×a+b) = χ(a,b).

Or if you want a definition without an explicit mention of χ:

(1) Copy Deedlit's entire definition of his M-based system (for reference: that's 5 lines).

(2) Replace every instance of χ(a,b) with I(M×a+b), adding a cavet that b must be smaller than M. (for reference: this requires changes only in lines 2 and 4).

And that's it. Now you have not just a definition of I(α), but an entire well-defined notation that uses it. This notation, of-course, is exactly isomorphic to Deedlit's notation.