User blog comment:Edwin Shade/Defining LOCC (Language Of Ordinal Construction)/@comment-5529393-20170929024107

I think there will be issues with doing things like defining T(a,b) and Z(b) but then defining Z(b) in terms of a. How do you know when a variable is a global variable or a dummy variable? It might be better to use a programming language to define your functions, augmented by commands and keywords for ordinals.

Your definition of T(a,b) and Z(b) only works for finite b; you need to define what happens at limit ordinals. I suppose you could have a convention that f(a) is always sup_{b<a}{f(b)} when a is a limit ordinal.

Anyhow, good luck!