Is a wife considered divorced if her husband swore to divorce her for not traveling and then denied it, and what is the ruling if he was lying in his denial?

The majority of scholars hold that swearing by divorce—whether the intention is to effect a divorce, threaten, or something else—results in divorce if the oath is broken. This is the prevailing fatwa. However, some scholars, such as Ibn Taymiyyah, are of the opinion that swearing by divorce without intending to make divorce conditional is treated like an oath sworn by Allah, requiring an expiation for an oath (kaffarat yamin) rather than leading to a divorce.

Therefore, if the husband swore by divorce intending to urge his wife to travel and not intending to effect a divorce, then there is a difference of opinion regarding whether a divorce occurs. The husband's statement is considered valid in matters of divorce when the spouses disagree, as long as he has not completed three divorces. The marital bond remains, and there is no sin upon the wife if the husband was not truthful, and she is not obliged to separate from him.