What is the ruling of Islamic law regarding a wife who has been divorced three times under the circumstances mentioned?

Divorce is not required in case of doubt, because the original state is the continuation of the marriage. If divorce is conditioned upon the occurrence of an action and that action does not occur, then the divorce does not take place. Likewise, if it occurs forgetfully, according to some scholars. However, if the wife deliberately performs the action upon which the divorce was conditioned, then the divorce takes place according to the majority of scholars. Ibn Taymiyyah, however, was of the opinion that an expiation for an oath (kaffarat yamin) is due if the husband did not intend divorce. If a divorce occurs, the wife can be taken back before the end of her waiting period ('iddah). As for the statement: "I will send you the divorce paper," if it is a promise, then nothing is binding. But if it is an initiation (of divorce), then it is effective. The second divorce takes place if the first one was not complete (i.e., not a triple divorce) and the wife was taken back; otherwise, it does not take place.