1) "HAFARAS NEDARIM" ON SHABBOS
QUESTION: The Gemara discusses whether a husband may annul the Neder of his wife on Shabbos when the Neder does not prohibit something necessary for the enjoyment Shabbos. The Gemara concludes that the Halachah depends on a Machlokes Tana'im with regard to the amount of time the Torah gives to a husband or father to annul the Neder. One Tana maintains that Hafarah must be done on the same day (until sunset) on which the husband or father hears the Neder, while another Tana maintains that Hafarah may be done at any point within a full 24-hour period after he hears the Neder.
The Mishnah (76b) permits Hafarah on Shabbos because it follows the view of the Tana who allows Hafarah only until sunset. Since, after sunset, the husband will not be able to annul the Neder because the day will have passed, the Rabanan permit him to annul it on Shabbos so that he not lose the opportunity of Hafarah. According to the other Tana, the Rabanan prohibit Hafarah on Shabbos since the husband can annul the Neder after Shabbos. The Ran (77a, DH Afilu, and 79a, DH she'Im) explains that this is the intention of the last line of the Mishnah: "he may be Mefer on Shabbos because if the sun sets he can no longer be Mefer." The Mishnah is giving the reason for why he may annul the Neder on Shabbos (i.e. so that he not lose the opportunity to do Hafarah).
The Rishonim disagree (see Insights to 69:1) about whether the husband's (or father's) Hafarah is limited to "Yom Sham'o," the day on which he heard the Neder, in a situation in which he was unable to do Hafarah on that day (for example, he divorced her in the middle of the day, or he lost the ability to speak in the middle of the day). The RAN writes that although he was unable to do Hafarah for part of the day, he still loses the ability to do Hafarah at the end of the day. The Yerushalmi explains that whether or not he loses the ability to do Hafarah depends on the dispute with regard to whether Hafarah may be done until sunset or whether it may be done for a full 24-hour period. If Hafarah may be done only until sunset of the day on which the husband hears of the Neder, then whether he loses the right of Hafarah when the day ends -- in a situation in which he was unable to do Hafarah -- depends on whether he had the ability to do Hafarah during the day. In contrast, if Hafarah may be done for a set amount of time (24 hours), he loses the right of Hafarah when that amount of time passes regardless of his ability to be Mefer. Both the Ran and the Yerushalmi agree that if a man does not know that he is able to annul the Neder, the day he hears of the Neder is not considered "Yom Sham'o" until he finds out that he has the right of Hafarah (79a); it is considered as though the day of "Yom Sham'o" never started (as opposed to where "Yom Sham'o" started but was stopped in the middle).
Why, then, would the husband lose his right of Hafarah after sunset on Motza'ei Shabbos if the Rabanan prohibit Hafarah on Shabbos? He is not able to do Hafarah on Shabbos, and, therefore, according to the Yerushalmi he certainly should be able to do Hafarah after Shabbos. Even according to the Ran, he should be able to do Hafarah after Shabbos since his "Yom Sham'o" never started since he did not have the ability to do Hafarah.
ANSWER: Perhaps, according to the Ran, the inability to do Hafarah does not extend the time during which one is allowed to do Hafarah. The only situation in which the time period for Hafarah is extended is where he did not know that he was able to do Hafarah. When the husband was unaware that he was able to do Hafarah, he is considered as though he did not hear the Neder since he did not understand what it meant to him. In contrast, if he heard the Neder when he did not have the ability to speak, or when he was not allowed to annul it because it was Shabbos, perhaps he loses the right of Hafarah once the day has passed.
According to the Yerushalmi, it is necessary to differentiate between a case in which a person is not able to do Hafarah (either physically, such as when he lost his voice, or Halachically, such as when he divorced her) and a case in which he is not permitted to do Hafarah. On Shabbos, even if he is not permitted to do Hafarah, if he transgresses the decree of the Rabanan and does do Hafarah, the Hafarah still takes effect (since mid'Oraisa he is permitted to do Hafarah on Shabbos). Therefore, he would lose his right to do Hafarah once the day of Shabbos passes. (See also ISHIM V'SHITOS 2:9, end of p. 115, on the view of the Rogatchover Ga'on.)

77b----------------------------------------77b

2) "HAFARAH" IN ONE'S HEART
QUESTION: The Gemara cites a Beraisa that states that a husband who wants to annul his wife's Neder on Shabbos should not use the usual formula for Hafarah and say, "It is annulled for you." Rather, he should say, "Take the item and eat," and the Neder becomes annulled. Rebbi Yochanan adds that the husband must annul the Neder in his heart as well.
The Gemara cites another Beraisa in which Beis Hillel says that on both Shabbos and a weekday it suffices for the husband to annul the Neder in his heart. He is not required to articulate his Hafarah verbally.
Why do Beis Hillel and Rebbi Yochanan maintain that the husband may annul the Neder in his heart? The Gemara later (79a) says that although Hakamah is effective when done in one's mind, Hafarah must be articulated verbally!
Moreover, why does Beis Hillel say that a husband may simply annul his wife's Neder in his heart, when the previous Beraisa states explicitly that he must also say, "Take the item and eat," which teaches that it does not suffice to annul the Neder in one's heart?
ANSWERS:
(a) The ROSH and TOSFOS in one explanation write that Hafarah indeed may be done in one's mind, like Hakamah. (See the Gemara on 76b which mentions a Hekesh between Hakamah and Hafarah.) When the Gemara later says that Hafarah cannot be done in one's mind, it means that it does not suffice to mentally want annul the Neder, but one must say the words in his mind, "It is annulled for you" ("Mufar Lechi") (see the Rosh's comments there). (See also Insights to Berachos 15:1b.)
The second Beraisa (in which Beis Hillel says that it suffices to do Hafarah in one's heart) means that although the Hafarah is accomplished through what the man thinks in his mind, nevertheless he must tell his wife that she should take and eat the food in order to inform her that he has annulled her Neder. By telling her in this manner he prevents slighting the honor of Shabbos.
(b) The ROSH in the name of RABEINU ELIEZER MI'MITZ explains that when Beis Hillel and Rebbi Yochanan say that one may annul the Neder in his heart, they mean that he must verbalize the Hafarah but he may say it so quietly that only he can hear it.
Beis Hillel does not mention that the husband must tell his wife to take the item and eat it, since those words are not part of the Hafarah but are merely to inform her that he has annulled her Neder and that she is allowed to eat the object (as mentioned in the previous answer).
(c) The RAN explains that although Hafarah cannot be done in one's mind, nevertheless if he says in his mind the correct wording of Hafarah and he openly enunciates a statement denoting Hafarah (but does not use the proper wording of Hafarah), the combination of what he thought and what he spoke is able to accomplish Hafarah.
The logic of the Ran's explanation might be that the reason why one is required to pronounce the Hafarah openly is merely to make the Hafarah a stronger, more deliberate decision (instead of letting it remain a mere thought). Therefore, if his words reveal that he has done Hafarah in his mind ("Machshavaso Nikeres mi'Toch Diburo") presumably with the correct formula, it suffices to use any wording to show that his decision was final.
According to the Ran, when Beis Hillel states that the husband may do Hafarah in his mind, he means that his thoughts are an effective form of Hafarah as long as he verbally articulates some indication of the intention in his mind (even though he does not articulate the formal wording of Hafarah).
What is the source for such a Hafarah, one which works without the proper formula having been articulated? A Neder formulated without the proper wording is not a valid Neder. Why should such a Hafarah be valid?
Perhaps the source that such a Hafarah works is the fact that Hakamah works in such a manner. Since Hakamah is valid even when done only in the mind without any speech, the requirements for Hafarah should not be very different. Even if speech is necessary for Hafarah, it should suffice to say something that reveals that he did Hafarah in his mind.
(d) The RAMBAM (Hilchos Nedarim 13:4-7, and in Perush ha'Mishnayos, end of this chapter) explains that there are two completely different methods which a husband may use to annul his wife's Neder. The first method is Hafarah, which cannot be done in the mind. The second method is "Kefiyah" ("forcing"): the husband tells his wife, "I want you to eat the item that you prohibited upon yourself." Whether she actually eats it or not, the fact that he tried to force her to eat it removes her Neder in the same way as Hafarah does.
"Kefiyah" is a stronger method of annulment of a Neder. The husband not only says that he does not want her to have the Neder, but he protests it by overriding the Neder and telling her to do what she said she would not do. Hafarah, on the other hand, merely shows that he does not want her to have a Neder upon her, but not that he specifically wants her to do the act she prohibited herself from doing. Since "Kefiyah" is a strong form of annulment, it is able to annul the Neder even if he merely thinks in his mind that he is going to force her. This form of annulment in his mind is referred to as "Bitul." (The Mishnah in Nazir (61a) mentions a similar concept of forcing a slave to transgress his Nezirus as a way for the master to remove his slave's Nezirus. However, the Mishnah there says that this method cannot be done with the Neder of one's wife. See RA'AVAD to the Rambam, ibid.)
According to the Rambam, why does Beis Hillel say that the husband may annul the Neder in his heart without saying "take the item and eat"? The Rambam (in Perush ha'Mishnayos) explains that Beis Hillel refers to a situation in which the husband is not able to force her at the present moment to do the prohibited action. In such a situation, it suffices for him to think in his heart that he annuls the Neder. If, however, he is able to force her, he should force her and think in his heart that he annuls the Neder.
The Rishonim reject the Rambam's explanation because they find no source for such a second method for a husband to repeal his wife's Neder.
Perhaps the Rambam's source for his ruling is the verse which uses two different words for the annulment of a Neder, "Hefer" and "Heni." The verse uses the word "Heni" when it discusses a father's annulment of his daughter's Neder (Bamidbar 30:6). It uses the word "Hefer" when it discusses a husband's annulment of his wife's Neder (30:12). The verse uses both "Heni" and "Hefer" when it discusses an Arus and a father who together annul the Neder of a Na'arah Me'urasah (30:9). According to the Rambam, perhaps the verses uses a different word for "annul" to refer to the more common method of annulling a Neder in each case.
The word "Heni," which is used in reference to the father's Hafarah, perhaps refers to the act of Bitul of the Neder, or "Kefiyah." Indeed, Rashi on the verse explain the word to mean, "He refuses her Neder to her." The normal method with which a father removes his daughter's Neder is "Kefiyah," since the nature of the relationship between a father and daughter is one of authority and deference. A husband, on the other hand, is not an authority figure to his wife and usually does not force her to comply with his wish. Rather, he removes her Neder through Hafarah. Accordingly, the Torah mentions "Hefer" only with regard to a husband and wife. In the case of a Na'arah Me'urasah, the girl is still young but somewhat independent, and thus the Torah uses both "Heni" and "Hefer," because both methods of annulment are common in that case. (M. Kornfeld)