Is it permissible to swear with the intention of the one taking the oath or the one for whom the oath is taken, and is equivocation permissible in an oath?

The oath is based on the intention of the swearer, if he intended something other than what he concealed, and his wording could bear what he intended, according to the saying of the Prophet, peace and blessings be upon him, "And indeed, every person will have what he intended." This is if his oath does not involve the right of another. However, if it involves the right of another, then the intention is for the one who administers the oath, according to the saying of the Prophet, peace and blessings be upon him, "Your oath is according to what your companion believes you to be truthful about."