What is the ruling on intercourse after a wife jokingly tells her husband, "Let's be siblings today," if they did not intend to make it forbidden?

The phrase mentioned does not result in ẓihār (a form of divorce) or prohibition, and the intercourse that occurred thereafter is permissible. For ẓihār to occur, it must be by an explicit utterance or an ambiguous utterance accompanied by the intention of ẓihār, neither of which was realized in this case.