1) "TUM'AS SHERETZ" IS "MERUBAH"
OPINIONS: The Gemara says that Tum'as Erev (Tum'as Sheretz) should apply to additional objects to which Tum'as Mes does not apply because it is "Merubah" -- it is "more." What does this mean?
(a) RASHI explains that there are "many" ("Merubah") types of Tum'os that last until the evening (Sheretz, Shichvas Zera, Maga Tum'as Mes, etc.), whereas only Tum'as Mes lasts seven days.
(b) RABEINU CHANANEL says that there are "many" -- i.e. eight -- types of Sheratzim to which Tum'as Sheretz applies, while there is only one type of Mes.
(c) The RASHBA cites RAV HAI GA'ON who says that Tum'as Sheretz is simply more common, since it is much more common for an object to become Tamei from a Sheretz than from a Mes.
2) TUM'AH AND HORSETAIL HAIRS
QUESTION: The Gemara says that not only can wool become Tamei, but even horsetail hairs can become Tamei. The Gemara points out, however, that the verse from which we learn that horsetail hairs can become Tamei is written with regard to Tum'as Sheretz. We cannot learn that horsetail hairs can become Tamei with Tum'as Mes from the fact that they can become Tamei with Tum'as Sheretz, because Tum'as Sheretz is Metamei more objects since its Tum'ah is "Merubah" (see previous Insight).
The Gemara then teaches that there is a Gezeirah Shavah that compares Tum'as Mes to Tum'as Sheretz in order to teach that a Mes will also be Metamei horsetail hairs. The Gemara adds that this Gezeirah Shavah is "Mufneh" ("open"; when the two similar words teach no other law, they may be used unconditionally for the inference of a Gezeirah Shavah between the two topics). If it were not Mufneh, we would not be able to derive that a Mes is Metamai horsetail hairs, because Tum'as Sheretz is more severe in that it is Metamei with the size of a k'Adashah (even a small amount of Sheretz, the size of a lentil, can be Metamei).
Why does the Gemara give a new reason for why Tum'as Sheretz is more severe than Tum'as Mes? The Gemara earlier said that Tum'as Sheretz is "Merubah," and that is why Tum'as Mes cannot be learned from Tum'as Sheretz. Now, however, the Gemara says that Tum'as Mes cannot be learned from Tum'as Sheretz because Tum'as Sheretz is Metamai b'k'Adashah. Why does the Gemara give two different reasons for why Tum'as Sheretz is more severe than Tum'as Mes?
(a) The MAHARSHA explains that there is a difference between the two reasons that the Gemara gives for why the Halachos of Tum'as Mes cannot be learned from Tum'as Sheretz. The reason of Metamei b'k'Adashah is stronger than the reason of "Merubah," because the reason of Metamei b'k'Adashah shows both that Tum'as Sheretz is more common, and that it is more severe. The Gemara uses this stronger reason at this stage in order to refute a Gezeirah Shavah, which is a strong Limud (as opposed to a Binyan Av, which is weaker).
However, according to the Maharsha's answer, why does the Gemara earlier ask a weaker question (that Tum'as Sheretz is "Merubah") and not the stronger question (that Tum'as Sheretz is Metamei b'k'Adashah)? Moreover, the Gemara has not yet concluded that the Limud is a Gezeirah Shavah that is Mufneh, and thus the Limud at this stage should be no stronger than a Binyan Av!
(b) The TOSFOS HA'ROSH explains that when the Gemara earlier says that Tum'as Mes cannot be learned from Tum'as Sheretz because Tum'as Sheretz is Merubah, it is not expressing the real reason for why Tum'as Mes cannot be learned from Tum'as Sheretz. The real reason is because Tum'as Sheretz is Metamai b'k'Adashah (as the Gemara itself says on 28a). The Gemara earlier was relying on the reason that it would express later. (A Beraisa does not always reveal its true reasoning, but it keeps it hidden. The Gemara that explains the Beraisa tells us the true reasoning of the Beraisa.)
3) HALACHAH: WOMEN AND WIGS
OPINIONS: The Mishnah says that a woman may go out on into Reshus ha'Rabim on Shabbos with hair tied around her hair, whether it is her own hair that is tied on or whether it is hair from someone else or from an animal. Similarly, says the Mishnah, a woman may go into a Chatzer (but not into Reshus ha'Rabim) with a Pe'ah Nochris (a wig). RASHI (here and in Erchin 7b) explains that the purpose of this wig is to give the appearance that the woman has a lot of hair.
(a) The SHILTEI GIBORIM proves from here that a woman is normally allowed to wear a wig in public, and that the Torah only requires her to cover the hair that is attached to her head. He explains that the Mishnah must be referring to married women, because the Gemara says that the reason she may wear certain articles (such as a wig) in a Chatzer is in order that she not become loathsome to her husband. This statement of the Mishnah also implies that the wig itself may be worn without a covering (because otherwise her husband would not be able to see it).
(b) The BE'ER SHEVA (Teshuvah #18) quotes RAV YEHUDAH KATZENELENBOGEN who explains that according to Rashi, who says that the purpose of a wig is to give the appearance that she has more hair, it is clear that the Mishnah maintains that a woman who wears a wig must wear it the same way other women wear their natural hair -- that is, covered.
We may ask, however, what is the point of wearing a wig that is covered if even her husband cannot see her hair? The answer is that the wig gives her hair a fuller look from beneath the kerchief. However, if the purpose of the wig is to stuff the kerchief, then why does the woman not simply stuff her kerchief with wool? The Rav Yehudah Katzenelenbogen answers that sometimes the kerchief slips from its place and the hair under it is visible, and it would be very embarrassing for wool to show up there instead of hair.
Second, Rav Yehudah Katzenelenbogen says that even if the Shiltei Giborim is correct that the wig is worn uncovered, perhaps it is worn uncovered only in a Chatzer (which is what the Mishnah is discussing) which very few people enter. In such a Chatzer where people do not commonly walk, a woman is permitted to go even with her natural hair uncovered, m'Ikar ha'Din. (This explanation seems a bit forced, for the Rishonim make it clear that a Pe'ah Nochris may not be worn in Reshus ha'Rabim only because of the Isur of Tiltul, and not because of the Isur of going out with uncovered hair; see Tosfos and Rishonim to 57b, DH Iy. -M. KORNFELD)
Third, even if the Mishnah is discussing a Chatzer where many people commonly walk, it is discussing only the laws of Shabbos and not the laws of modesty and Das Yehudis. That is, from the perspective of the laws of Shabbos, a woman may go into a Chatzer with an uncovered wig (while from the perspective of the laws of Das Yehudis, she may not). He points out that this is similar to what the Rosh writes at the beginning of Shabbos (end of 1:1) with regard to "Lifnei Iver." (This proof also seems forced, since the Rabanan permitted the woman to wear the Pe'ah Nochris in order that she should not appear loathsome to her husband, which implies that it is a proper thing for a woman to do.)
We may suggest another reason why a woman covers the hair of her Pe'ah Nochris. The main purpose of the Pe'ah Nochris may be to appeal to her husband when in the house, where a woman is permitted to leave her hair uncovered. However, since it was complicated to put on and remove a wig in the times of the Gemara, the woman would often leave the wig on even when she went into Reshus ha'Rabim, and she would cover it in accordance with the requirement to cover her hair.
In any case, Rav Katzenelenbogen concludes that it is forbidden to wear a wig without covering the wig's hair.
HALACHAH: The MAGEN AVRAHAM (OC 75:5) sides with the Shiltei Giborim and permits a woman to wear a wig without covering the wig's hair. In practice, there are various customs among different communities, and one should follow the custom of her community or consult with a competent rabbinical authority..
4) HALACHAH: WOMEN WEARING JEWELRY AND OTHER ORNAMENTS ON SHABBOS
OPINIONS: The Mishnah here (and on 57a and 62a) lists a number of decorative objects with which a woman may not go into Reshus ha'Rabim (or, in the case of most of the objects mentioned, even into a Chatzer) on Shabbos out of concern that she might carry them four Amos in Reshus ha'Rabim.
The Gemara quotes Rav, who rules in accordance with the Mishnah. The Gemara then cites another Tana in a Beraisa, Rebbi Anani bar Sason in the name of Rebbi Yishmael bar Rebbi Yosi, who permits a woman to go into a Chatzer with all of the things listed in the Mishnah. What is the Halachah?
There are five opinions among the Rishonim.
(a) The RAMBAN and RASHBA rule that a woman may not wear these items into a Chatzer, as the Mishnah says. They add that a house is no different than a Chatzer, and thus a woman is prohibited to wear these items even inside of her house. However, she may carry* these items in a house or Chatzer, as long as she does not wear them.
(b) The RAMBAM (Hilchos Shabbos 19:8) also rules like Rav, that one is prohibited to wear these items in a Chatzer. However, he adds that the prohibition applies only to a Chatzer she'Eino Me'ureves, a Chatzer that needs an Eruv but does not have one. In a Chatzer Me'ureves (that has an Eruv) or in a house, a woman may wear these items.
(c) The TUR (OC 303) quotes RABEINU TAM who says that the Halachah follows the view of Rebbi Anani, and a woman is permitted to wear these items even in a Chatzer that has no Eruv.
(d) The SEFER HA'TERUMAH (RABEINU BARUCH) cited by Tosfos and the Tur rules like Rebbi Anani and permits a woman to wear these items not only in a Chatzer that has no Eruv, but even in a Karmelis. Although Rebbi Anani does not mention a Karmelis (which implies that he prohibits wearing these items in a Karmelis), his view applies only in those days, when there were places which had the status of an actual Reshus ha'Rabim. In our times, though, there is no area that is an actual Reshus ha'Rabim, and therefore a woman is permitted to wear jewelry even into a Karmelis. (An object that does not have the status of an ornament, but the status of a load that one carries, may not be taken into a Karmelis, of course. The Sefer ha'Terumah permits going out only with those items that a woman wears but might take off to show to her friends.) Therefore, nowadays a woman may wear these items on Shabbos anywhere.
(e) RABEINU SHIMSHON, as cited by Tosfos and the Tur, suggests another reason for why a woman may walk out while wearing jewelry on Shabbos in our times. In the days of the Mishnah and Gemara, women used to show off their jewelry. Nowadays (when women wear jewelry both on Shabbos and during the week), women do not usually take off their jewelry to show off to each other, and thus women are permitted to wear jewelry anywhere.
The ARUCH HA'SHULCHAN (OC 303:22) adds that in our times, all women are considered distinguished ("Chashuvos") and they consider it beneath their dignity to remove their jewelry to show it off. Furthermore, in those days, the women did not go out often, and on the rare occasion that they went out, they would wear all of their jewelry to show to their friends. Since women did not go to the synagogue, there was a serious concern that they would take off their jewelry in Reshus ha'Rabim to show to each other. In our times, women go out often and meet each other in their homes or in the synagogues, and thus there is no fear that they will remove their jewelry in Reshus ha'Rabim to show to each other.
HALACHAH: The SHULCHAN ARUCH (OC 303:18) cites the first four opinions, and the REMA cites the fifth. The Shulchan Aruch also mentions the conclusion of TOSFOS (DH Rebbi Anani) and the ROSH (6:10), who say that it is better not to stop the women from wearing these items outside on Shabbos even when it is prohibited, because it is unlikely that they will listen and it is better that they transgress unknowingly than willfully.