User blog comment:Denis Maksudov/Slowly growing ordinal function and FS up to BHO./@comment-28606698-20170402064919/@comment-1605058-20170402100857

It should be noted that this is not so under what one usually means with "fundamental sequence", which is usually defined as an ordinal sequence of length \(\omega\) supremum of which is the given ordinal. You need to allow sequences of greater length.