Is it permissible for a man to annul his first marriage contract (without uttering a divorce) in order to marry a second woman, due to the law prohibiting polygyny, while the first wife remains his legal wife in religious terms only, and does the first wife have the right to seek a divorce in this situation, which might expose her to legal and social problems?

There is no harm for a man in using allusive phrases that imply divorce to official bodies, if he intends not to enact it. It is commendable for him to have two witnesses attest to his intention, in order to preserve his right to polygyny; this is known as istir'aa'. If the first wife is harmed by this, she has the right to seek divorce. However, if she does not fear harm, it is not permissible for her to seek divorce merely due to polygyny.