Without an eruv, can a woman walk out with ear-rings? Thanks.
We are copying our Insights to the Daf- Shabbos 64:4 that pertains to your question.
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Shabbos 64
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.