The u.k. are adamant that there should not be a border between northern and Southern Ireland in the wake of Brexit, but an eu outer border has to appear somewhere and northern Ireland are either in or out. The acting MP for northern Ireland in Westminster has stated that the north stays with Britain unless they want to do otherwise. In view of this why not formally invite the north to join Ireland instead of waiting passively for more unlikely deals? Their acceptance or refusal would then demark the border.