Gemara

34b (Mishnah): A widow collects her Kesuvah from orphans' property only by swearing (that she did not already receive her Kesuvah). Judges refrained from administering the oath. R. Gamliel enacted that she vow like the orphans desire, and then collect.

35b (Rav Huna): She may vow only if she did not yet remarry. If she already remarried, she does not vow.

She may not vow, for surely her husband will annul the vow. She may vow before remarrying, for a husband cannot annul vows she made before he married her.

Question: We should be concerned lest she vow falsely, expecting that she will regret her vow in Beis Din, and Beis Din will permit it!

Answer: Rav Huna holds that one who asks to permit a vow must tell Beis Din the details of the vow. Therefore, Beis Din would not permit it.

(Rav Nachman): She collects through a vow even after she remarried.

Question: She is not afraid to vow falsely, for her husband will annul the vow!

Answer: She vows b'Rabim (in front of many. Her husband cannot annul this.)

Question (Beraisa): If she remarried, she vows and collects her Kesuvah.

Answer: Tana'im argue about whether or not a husband can annul a vow made b'Rabim. (This Tana holds that he cannot.)

(Rav Nachman): If one seeks to permit a vow, he need not give the details.

If he needed to, sometimes he would omit a detail, and the Heter (permission) would be Pasul, since Beis Din permits only what they hear!

(Rav Papa): He must give the details.

We are concerned lest he seeks to permit a vow in order to transgress!

(Mishnah): A Kohen who marries a woman forbidden to Kohanim is disqualified from serving in the Mikdash until he vows not to benefit from her.

(Beraisa): He may serve once he vows. After serving, he divorces her.

Question (against Rav Nachman): If one may permit a vow without detailing it, perhaps he will permit his vow and keep his wife!

Answer #1: He must vow b'Rabim.

Answer #2: According to the opinion that a vow b'Rabim can be permitted, he vows Al Da'as Rabim (i.e. the vow is contingent on the consent of others);

(Ameimar): The Halachah is, even the opinion that allows permitting a vow b'Rabim, does not allow permitting a vow Al Da'as Rabim.

Rishonim

Rif and Rosh (4:8): Rav Huna permits her to vow before remarrying. A husband cannot annul her vows from before he married her. After remarrying she cannot vow, for surely her husband will annul it. The Halachah is, even the one who allows permitting a vow b'Rabim does not allow permitting a vow Al Da'as Rabim.

Rambam (Hilchos Ishus 16:12): If the widow died before swearing, her heirs do not inherit her Kesuvah, for she does not collect until she swears. If she remarried before swearing, she swears after the Nisu'in and collects whenever she wants. She cannot vow and receive, lest her husband annul it.

Rosh: Even after she remarried, we could make her vow not to eat a loaf if she received from her Kesuvah, and then she will eat it in front of us! We must say that only a permanent Isur deters her.

Suggestion: She can vow Al Da'as Rabim, which cannot be annulled!

Rejection (Rosh): A husband can annul it, for a woman vows Al Da'as her husband. She cannot uproot this. Perhaps it does not help even if her husband permits her to vow on the Da'as of others. This is unlike when he affirms her vow. One who affirms can regret (and undo) his Kiyum, and then annul her vow.

Rosh (10): Rav Huna requires detailing the vow to permit it. If he did not, even b'Di'eved it is not permitted. The Halachah follows Rav Papa, who obligates detailing, for he is Basra. Also, Rav Huna supports him, and the Yerushalmi connotes that this is the Halachah.

Poskim

Shulchan Aruch (EH 96:19): A vow helps only before she remarried. She may not collect through a vow after remarrying, for her husband will annul it.

Beis Yosef (DH v'Lo): The Rif, Rambam and Rosh rule like Rav Huna, that she may not vow after she remarried.

Question (Birkas ha'Zevach): A Kohen who married a woman b'Isur may serve immediately after vowing not to benefit from her. The opinion that does not require detailing the vow obligates him to vow Al Da'as Rabim, lest a Chacham permit it. The Shulchan Aruch (YD 228:14) obligates detailing the vow. Why must a Kohen who married b'Isur vow Al Da'as Rabim? (OC 128:40)?

Answer #1 (Magen Avraham 128:58): Amora'im argue about whether or not one must detail the vow. The Gemara did not say whom the Halachah follows. The Rambam and Rashba are concerned lest a Kohen go to a Chacham who does not require detailing the vow.

Machatzis ha'Shekel (DH Chosheshu): Rav Papa holds that in the days of the Mishnah all required detailing the vow, therefore the Mishnah does not require Al Da'as Rabim. Nowadays that some do not require detailing, one must vow Al Da'as Rabim, lest a Chacham hold like the lenient opinion.

Magen Avraham: Even though we do not obligate a widow to vow Al Da'as Rabim, we are more stringent about Isurim.

Machatzis ha'Shekel (DH v'Yesh): The concern lest a Chacham be lenient unlike the Shulchan Aruch is far-fetched, therefore we are concerned only regarding Isurim.

Answer #2 (Magen Avraham): Tosfos (Erchin 23a DH Mar) says that the opinion that obligates detailing the vow requires only saying all the words, but he need not say why he vowed. The Rashba and Shulchan Aruch hold that one must say why he vowed, but they are concerned lest a Chacham who holds like Tosfos hear the vow 'I will not marry a divorcee' without hearing the reason or knowing that he is a Kohen. One who hears that a widow vowed 'Peros are forbidden to me if I benefit from my Kesuvah' will not permit it.

Pri Chodosh (Mayim Chayim on Gitin 34b, cited by R. Akiva Eiger): The Rambam does not require detailing the vow, only to say what he vowed about. This is why a Kohen must vow Al Da'as Rabim. The Gemara was concerned lest a widow permit her vow, and answered that one must detail the vow. The Rambam does not rely on this answer. Rather, one who vowed benefit from Ploni may permit it only in front of Ploni. We are not concerned lest a Chacham permit her not in front of the orphans. This does not answer for the Shulchan Aruch, which requires detailing also the reason for the vow!