Question

Hello Rabbi,
I heard that a few months ago the Rabbi officiated at a wedding in which there were several conditions. One of the conditions was that the woman not commit adultery.
The simple understanding I have had until now is that the whole essence of kiddushin is to forbid the woman to the entire world (and it seems that even the literal meaning hints at this). In this case, however, in practice there is no reality in which the woman becomes forbidden to another man, since if another man has relations with her there would be no prohibition, because it would turn out that she is not a married woman. This seems comparable to a case in which the man making the kiddushin stipulates that she is not forbidden to the whole world, and as is known, in that case his condition is void. One can, admittedly, distinguish between the cases, but still, if the very essence of kiddushin is the prohibition vis-à-vis the rest of the world, then in this case the woman was not forbidden, and therefore she was not betrothed/married (or else the condition is void).
Of course, one could answer and say that the woman is now indeed forbidden to the whole world as a married woman, except that if she cheats it will become clear that she had never been a married woman at all. The fact that there is no practical difference regarding the prohibition does not mean that this prohibition did not take effect upon her. That does seem to have some logic to it, but it is a very great novelty and not at all simple. I would like to know whether it was on this reasoning that the Rabbi relied in arranging this kiddushin, and if not, I would be glad to hear another explanation.
Thank you, and Sabbath שלום,
Yair