User blog comment:Rgetar/Shellcore notation/@comment-35470197-20190108134644

> Let "string" is sequence of natural number of ordinals.

What does "natural number of ordinals" mean?

> Strings are enumerated using ordinals in increasing order, beginning from 0.

> What is limit of this notation (if we use only "[" and "]")?

How could you verify the well-foundedness of the comparison of strings without knowing the limit? If you do not have the well-foundedness, the enumeration does not induce a correspondence to ordinals.