Gemara

46b Question (Rami bar Chama - Beraisa): Vows may be annulled [by a husband] on Shabbos, for the need of Shabbos.

Even if a vow [not to eat a food] is annulled, the food should be forbidden, for she did not plan to eat it. Nothing suggests that her husband will annul it!

Answer: She expects her husband to annul it, like Rav Pinchus taught;

(Rav Pinchus): A woman vows on condition that her husband will agree to it.

Question (Mishnah): One may ask [a Chacham] to permit vows on Shabbos, if they are for the need of Shabbos.

The food should be forbidden, for she did not plan to eat it. Nothing suggests that she will find a Chacham to permit it!

Answer: If she does not find a Chacham, she can get three commoners to permit it.

47a (R. Yochanan): R. Rumnus said that Rebbi permitted him to move an incense pan with ashes in it.

(R. Asi): The case is, there are also sticks of frankincense left in the pan.

Objection (Abaye): Sticks of frankincense are of no significance in the house of Rebbi! (He was very rich.)

Suggestion: Perhaps because they are significant for Aniyim (poor people), they are significant for everyone!

Rejection (Beraisa): Bigdei (clothes proper for) Aniyim (e.g. cloth three by three fingers) are Mekabel Tum'ah (Tosfos - of Mishkav u'Moshav) if an Oni owns them. Bigdei Ashirim (of rich people, e.g. three by three Tefachim) are Mekabel Tum'ah if an Ashir owns them.

Inference: Bigdei Aniyim are not Mekabel Tum'ah if an Ashir owns them!

125a (R. Zeira): One may not move a worn out Talis on Shabbos.

(Abaye): He refers to rags less than three by three fingers, since they are not useful for rich or poor people.

127b (Mishnah): We may clear out Tahor Terumah.

Since Kohanim may eat it, anyone may move it.

Rishonim

Ran (21a DH umi'Ha): Our Gemara teaches that Muktzeh for Ashirim is Muktzeh, and even Aniyim may not move it, for the rich owner already diverted his mind from it. It need not be Muktzeh for everyone. Also 46b connotes like this. We may annul and permit vows for the need of Shabbos. The Gemara asked that the food should be forbidden, for she did not plan to eat it, for she did not know that her husband will annul, or that she will find a Chacham to permit it! This shows that since she forbade the loaf to herself, it becomes Muktzeh.

Tosfos (46b DH Mi (2)): Even though Peros from which one vowed are not Muktzeh regarding moving, for they are permitted to other people, we should say that just like he was forbidden to eat them Bein ha'Shemashos, he is forbidden the entire day. Alternatively, we discuss her Peros, and she forbade them to everyone.

Tosfos (127b DH Kivan): Even though we say that Bigdei Aniyim are not Mekabel Tum'ah if an Ashir owns them, here the Terumah is [physically] proper for everyone to eat, just there is an Isur [to Yisre'elim]. There, the Bigdei Aniyim are [physically] improper for Ashirim. This is why there we do not say that it helps to make his property Hefker. One may not move remnants of a Talis less than three by three fingers, but if they are three by three, one may move them, i.e. an Oni may. Alternatively, even Ashirim in an Oni's house may.

Shiltei ha'Giborim (21b:1): Tosfos (46b) says that a vow forbids only to the person, but not to others. I agree. We find what is Muktzeh to one is not Muktzeh to all others. Tosfos 127b says that if something is Muktzeh to Ashirim due to inferiority, it is permitted to Aniyim, and even to Ashirim in an Oni's house.

Rebuttal (Magen Avraham 308:79): Tosfos 127b agrees that if an Ashir owns it, it is Muktzeh even for Aniyim. Since it is Muktzeh due to inferiority, it depends on the owner's opinion. Tosfos argues with the Ran only regarding Muktzeh due to an Isur. He holds that it is not Muktzeh, and even the one who vowed may move it.

Poskim

Shulchan Aruch (OC 308:7): If a piece of earthenware broke from a Kli during the week, and it is proper to use to cover a Kli... If he threw it to the wasteheap before Shabbos, one may not move it, since he was Mevatel it from being a Kli.

Rema: Even if it is proper for an Oni, since the owner diverted his mind from it, even though he is an Ashir, Muktzeh for Ashirim is Muktzeh for Aniyim, like it says in Sa'if 52 (below).

Shulchan Aruch (52): Muktzeh for Ashirim is Muktzeh, and even Aniyim may not move it.

Bach (8 DH Kasav): Muktzeh for Ashirim are things like fabric less than three Tefachim by three Tefachim, or sticks of frankincense. They are not important to an Ashir, so he diverted his mind from them. Even Aniyim may not move them. Surely this is only for Aniyim in the Ashir's house, since the rich owner diverted his mind from them. This is clear from the Gemara. Abaye asked 'sticks of frankincense are of no significance in the house of Rebbi! Do not say that since they are significant for Aniyim, they are significance for everyone. Bigdei Aniyim are Mekabel Tum'ah if an Oni owns them, and Bigdei Ashirim are Mekabel Tum'ah if an Ashir owns them, but Bigdei Aniyim are not Mekabel Tum'ah if an Ashir owns them! Also here, sticks of frankincense are insignificant in Rebbi's house! They are Batel, and [the pan of ashes is] forbidden even for Aniyim in Rebbi's house. They are not Muktzeh for Aniyim not in Rebbi's house. Surely what is Muktzeh for one person is not Muktzeh for the entire world! Therefore, a garment three by three fingers is not Muktzeh in an Oni's house. If three by three fingers of a Talis remains, one may move it, i.e. in an Oni's house. It is not Muktzeh even for Ashirim in an Oni's house. It all depends on the owner's opinion. Tosfos (127b) explicitly says so. Tosfos (46b) says that if one forbade Peros through a vow, they are not Muktzeh even to him regarding moving, for they are permitted to others, unless he forbade his Peros to everyone. This is like we say that a Yisrael may move Tahor Terumah. It is proper for all, just there is an Isur on it.

Rebuttal (Taz 25): The Ran connotes that what is Muktzeh for Ashirim is Muktzeh for all Aniyim in the world. It depends on the owner. Abaye said Stam 'for Aniyim.' He did not say 'Aniyim in the house.' Tosfos (127b) says that one may move remnants of a Talis less than three by three Tefachim, i.e. an Oni may move it, or even Ashirim in an Oni's house. That depends on the house. It is Muktzeh for Ashirim outside the house, for it is not useful for them. It is proper for an Ashir in an Oni's house, since it is useful in the house. This is unlike something Huktzeh to an Ashir. It is as if he threw it in the wasteheap (Sa'if 7). We do not say that if one takes it from the wasteheap, it is useful for him. Therefore, it is Muktzeh even for Aniyim outside the Ashir's house. If we would permit to Aniyim outside the Ashir's house, why was the question from Rumnus? Perhaps he was permitted because he was outside Rebbi's house! Rather, it is forbidden to all Aniyim. The Ran derives that Muktzeh for Ashirim is Muktzeh for Aniyim. The Shulchan Aruch rules like this. What is proper for Aniyim in an Oni's house is Muktzeh for Ashirim, since it is not useful for them. However, someone in an Oni's house, even an Ashir, is drawn after the house.

Mishnah Berurah (170): It is Muktzeh even for Aniyim outside his house. It depends on the owner's opinion. Sa'if 13 permits remnants three by three fingers, i.e. of an Oni. The Taz permits only for an Ashir in an Oni's house. The Poskim say that Muktzeh to the owner is Muktzeh to all only if it is due to inferiority, but not if it is due to an Isur.

Kaf ha'Chayim (282): Ma'adanei Yom Tov, the Bach and Shiltei ha'Giborim permit to Aniyim in their own houses. The Taz, Magen Avraham and others disagree.