User blog comment:PsiCubed2/Counting with Ordinals/@comment-32876686-20171208202657

What is the precise meaning of enclosing a structure within square brackets in a box visualization ?

I ask this because it seems that for the beginning of the box visualizations, $$[S_1]\cong\omega^{S_1}$$, where $$S_1$$ is a structure equivalent to some ordinal $$\alpha<\varepsilon_0$$. However, [⟅●⟆] is equivalent to $${\varpsilon_0}\omega$$, rather than $${\omega^{\varepsilon}}$$. The brackets appear to change meaning after the structure they enclose is greater than or equal to $$\varepsilon_0$$. This makes me wonder if perhaps the box visualizations are employing an ordinal collapsing-esque way of representing ordinals, is this so ?