In article <email@example.com>, WM <firstname.lastname@example.org> wrote:
> There is no term s_n of S that contains all natural numbers. This > condition requires > (2) exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k.
Nothing outside of Wolkenmuekenheim implies "(2) exist j, k, m, n : m e s_j & ~(m e s_k) & ~(n e s_j) & n e s_k" though it is implied often enough enough inside Wolkenmuekenheim.
Note that when each "a_k" is regarded as representing the set of naturals up to and including k, if (2) were true outside of Wolkenmuekenheim, one would have both j < k and k < j simultaneously true as well. What its truth inside of Wolkenmuekenheim would mean is beyond the ken of those of us fortunately forever outside its walls. --