User blog comment:Tetramur/The new formalization of BEAF/@comment-35470197-20200222073359/@comment-35470197-20200222101942

> So, valid expressions are obtained by applying symbol &n to some structure for any natural number n (n = 1,2,3,4,5,...).

> Structure is some expression using X and natural numbers.

It implies that if a is a valid expression, then a&1 and a&1&1 are valid expressions. Is it correct?

> Homogeneous structure is such a structure that doesn't have a finite natural number as last term in its expression.

The terminology "term" is undefined for your notation.

> For example, X^^X and X^^^^(X^7) are homogeneous. If the structure isn't homogeneous, it is inhomogeneous. X^^X + 9 and X^^^^(X^7) + 17 are both inhomogeneous.

They are not valid expressions in your definition.