User blog comment:Deedlit11/Is BEAF well-defined?/@comment-25418284-20121121205547

Okay, here's a crazy idea: how about using Cantor's ordinals? \(X\) structures behave a lot like \(\omega\), and we could use them as a concrete ground for formally defining BEAF.

We could describe positions of entries using ordinals. The entries on the first row are on positions \(0, 1, 2, 3, \ldots\), then we use \(\omega\) to label the next row: \(\omega, \omega + 1, \omega + 2, \omega + 3, \ldots\). The next plane starts on \(\omega^2\), the next realm on \(\omega^3\), the next dimensional group on \(\omega^\omega\), ...