If one divorces his wife, and then engages in sexual relations with her before witnesses --italics: or it is evident to everyone that he engaged in sexual relations with her, like he married her (the Ran in the chapter titled "Every Get"-- before she married another, whether he divorced her from betrothal or marriage, since she was his wife, we assume that he took her back [as his wife] and for the sake of marriage he engaged in relations [with her] and not for prostitution. And even if they saw that he gave her money, for there is an assumption that a person doesn't engage in sexual relations for prostitution, and it's in his capability to make these sexual relations for a commandment [that is, for marriage purposes]. Therefore, this [woman] is definitely married, and requires a second get (that is, divorce document).
If he was alone with her before two witnesses, and the two witnesses [testified] as one, and he and she saw the witnesses, if she were divorced from marriage, we are concerned that they had sex, and the witnesses of their being alone are witnesses that they had sex. Therefore, there is doubt as to whether this constitutes a marriage, and she requires a bill of divorce out of uncertainty. If she had been divorced from betrothal, we are not concerned about her, for he does not desire her. If we see that they do desire each other, we are concerned about her. Rem"a: If he was alone with his match, even though he desires her, we are not concerned, unless he had sex with her before witnesses (Responsa of the Ramba"n #135).
One who sent a bill of divorce, and nullified it afterward, and went and was alone with her, and afterward to became clear that she already received the bill of divorce before his nullification, she does not require a second bill of divorce from him, for he certainly would not have had sex with her for the purposes of betrothal, for he believed that the bill of divorce had been nullified, and he only had sex with her by virtue of the original betrothal.
One who divorces his wife and secludes himself with her, and before he divorces her a second time [out of doubt whether the seclusion constituted marriage], another man took her as a concubine, she is forbidden from both of them and requires a bill of divorce from both of them.
They only stated this presumption that a man does not intend sexual intercourse for licentious purposes regarding his wife whom he divorced or one who betrothed on condition and subsequently had intercourse without restating the condition, for she is his wife and regarding his wife it is presumed that he is not having licentious intercourse unless he states explicitly that it is licentious intercourse or he states explicitly that he is having sex on condition. But all other women it is presumed that he has sex with them licentiously until he states explicitly that he had sex with them for the sake of betrothal.
Likewise, a man or woman who converted [to another religion] under the duress of the decrees, and married each other under non-Jewish law, even though they are secluded with each other daily in front of everyone, one needn't be concerned that they have done formal betrothal. (And see above ch. 26.)
Someone who is secluded with his wife after he instructed a divorce document to be written, signed, and delivered to her, they should not write [the divorce document]. And if they wrote and gave it to her after he was secluded with her, she is a doubtful divorcee.