Shulchan Arukh Even HaEzer · Siman 150

English

Any get (that is, divorce document) that is nullified on a Torah level, if she is divorced with it, she is still a complete married woman. And if she married with it, she must leave [the second husband] and the child [that she had with the second husband] is a mamzer (born of an illicit sexual relationship), and she requires a get from the second [husband] on a rabbinic level, and from the first [husband] on a Torah level, to permit her to [other men in the] world. And she is forbidden to both of them forever. And all of the thirteen ways that we treat a woman whose husband went to a foreign country and she married [another] and then afterward her husband came, that are explained in Section 17, we apply to her [this woman]. --Italics: And there are those that say that the first husband inherits her (The Magid Mishna Chapter 10 of [the laws of] Divorce)-- However, if she still hasn't married, but she became betrothed, she is permitted to her [first] husband, and she does not require a get from the second. And any get which is only unfit to marry with on a Rabbinic level, she may not marry with it a priori. But if she married, even if she did not engage in intercourse, she does not leave [the second husband] and the child is kosher (that is fit, not a mamzer). And they write for her another get [from the first husband] and she lives with her [second] husband. And if it is impossible to write [another] get for her, and the [second] husband was righteous and divorced her on his own, that is praiseworthy. When does this? When he doesn't have children from her. However, if he has children from her, he should not release [her], for it brings slander upon the children. --Italics: However we give another valid get and there is no issue of bringing slander upon the children (Rulings of Mahara"y section 21). Anything that we are strict [about] with gitin (plural of get), and the get is valid without it, but we are stringent to write it [this way] a priori, if it is not written [this strict way], then the get is valid (Mahariy"o section 23).

English

As long as a women status as being divorced is in doubt, she should not marry. If she marries, she should be released and her child will be considered bastard.

English

Any Get (writ of divorce) that is nullified from the Torah, if her husband was a Cohen she was not forbidden to him because of divorce, except for the divorcer and says to her: "Behold you are divorcing from me and you are not permitted to all men, that even though there is no Get here at all, you are disqualified to Kehuna (marrying a Cohen)."

English

One who divorced his wife with a divorce certificate containing a flaw (invalid), or if it was doubtful that she was indeed divorced and he wished to reverse the process, he must repeat the blessing of marriage, but he is not required to recite the "seven blessings" or to write her a new marriage contract.