The Shulhan Aruch (Eben Ha’ezer 18), based on the Gemara’s discussion in Masechet Kiddushin (67), writes that if a person attempts to marry a woman forbidden to him by the Torah on the level of a capital offense, the betrothal does not take effect. For example, engaging in relations with one’s sister is punishable by Karet (eternal excision from the Jewish people). Therefore, if a person betroths his sister, even if he gives her an object of value in the presence of two valid witnesses and says, "Hareh At Mekudeshet Li" ("You are hereby betrothed to me"), the betrothal does not take effect. The man and his sister are not considered married. This applies as well to marriages that are punishable by Mitat Bet Din (court-administered execution). Even if the Kiddushin (betrothal) was done according to all Halachic requirements, it has no effect at all, and the man and woman are not considered married.
Any children born to these kinds of marriages have the status of Mamzer. If a couple who is forbidden to each other on the level of Karet or Mitat Bet Din have a relationship and beget children, the children are Mamzerim.
However, there are certain marriages which the Torah forbids on the level of a "Lav," meaning, as an ordinary Torah prohibition, without carrying the punishment of Karet or Mitat Bet Din. For example, the Torah forbids a Kohen from marrying certain kinds of women, such as a divorcee, but this violation is not punishable by Karet or Mitat Bet Din; it is an ordinary Torah prohibition. As such, if a Kohen betroths a divorcee, and the betrothal is performed in accordance with Halachic procedures, then it is binding, and the couple is considered married. Even though they have transgressed the Torah, the marriage takes effect. Therefore, if they repent, they must dissolve the marriage through the giving of a Get. Children born from such a union are not considered Mamzerim, since it does not entail a violation on the level of Karet or Mitat Bet Din.
An exception to this rule is a case of "Yebama La’shuk." If a man dies without children, the widow is obligated to either marry the deceased’s brother, or perform the ritual of "Halisa" with him. She is forbidden to marry anybody else until she either marries the brother-in-law (and he subsequently divorces her and dies) or performs Halisa. If she does marry another man, she has transgressed a Torah violation that does not carry the punishment of Karet or Mitat Bet Din. Nevertheless, the Sages enacted a provision that in such a case the betrothal has the status of "Safek Kiddushin" – meaning, it is uncertain whether or not it takes effect. Although marriages that are forbidden on this level are generally considered bona fide marriages, the Sages made an exception in the case of "Yebama La’shuk" and said that the betrothal should be treated as though we are in doubt regarding its validity.
The Aruch Ha’shulhan (Rav Yehiel Michel Epstein of Nevarduk, 1829-1908) raises an interesting question regarding this principle (listen to audio recording for precise citation). There is a rule in Halacha known as "Kol De’mekadesh Al Da’ata De’Rabbanan Mekadesh," which means that when a man betroths a woman, the betrothal is done on the implicit condition of the Rabbis’ consent. The Gemara gives several examples of cases where, due to certain circumstances, a marriage is automatically dissolved, without a Get, by force of this rule. Since betrothal is done on the implicit condition that it meets the Rabbis’ approval, it is automatically dissolved in situations in which the marriage does not meet the approval of the Hachamim. If so, the Aruch Ha’shulhan asks, then how can there ever be a situation of a forbidden marriage where the Kiddushin is valid? By definition, any forbidden marriage is objectionable to the Rabbis. In light of the rule of "Kol De’mekadesh Al Da’ata De’Rabbanan Mekadesh," then, it should be automatically void, since the Kiddushin does not meet the Rabbis’ approval. Why, then, is a forbidden marriage considered binding if the prohibition does not involve Karet or Mitat Bet Din? Why is it not automatically void?
The Aruch Ha’shulhan explains that the rule of "Kol De’mekadesh" means that if a marriage was done properly, in accordance with Halacha, then its status henceforth is dependent upon the Rabbis’ approval. In the case of a forbidden marriage, the betrothal was clearly not made with an implicit condition that it meets the Rabbis’ approval. It never came under the Rabbis’ jurisdiction, because it was not done subject to their approval. But in the case of a proper marriage, there is an implicit condition that the marriage is valid only with the Rabbis’ approval, and therefore, in certain circumstances, the marriage is dissolved due to problems that have arisen. This condition is implicitly made only if the marriage was in accordance with Torah law. In the case of a forbidden marriage, however, the marriage was not done on condition of the Rabbis’ approval, and it can therefore be binding in certain cases.
Summary: If a man marries a woman forbidden to him on the level of a capital offense, such as in the case of incest or adultery, they are not considered married, even if the betrothal followed Halachic procedures. They thus do not require a Get, and children born from such a union are Mamzerim. If the prohibition is not a capital offense, such as in the case of a Kohen who marries a divorcee, the marriage is binding and the couple therefore needs a Get. Children born from such a marriage are not Mamzerim.
