Gemara

(Mishnah - R. Yehudah): (Chachamim enacted Pasei Bira'os. If four L-shaped corner-posts [of a certain size] surround a well, one may take from the well and carry inside the posts.) If Reshus ha'Rabim passes through the posts, it must be diverted.

Chachamim say, there is no need for this.

Contradiction (Beraisa - R. Yehudah): If one owns two houses on opposite sides of Reshus ha'Rabim, he puts a Lechi (vertical post) on each side or a Korah (horizontal beam) on each side, and he may carry in the middle.

Chachamim: We cannot be Me'arev Reshus ha'Rabim like this!

Answer: R. Yehudah permits to be Me'arev when there are two proper walls. None of the walls of Pasei Bira'os are proper;

Chachamim permit Pasei Bira'os because there are four Mechitzos. There, there are only two Mechitzos.

(R. Yochanan and R. Elazar): This (Chachamim's opinion) teaches the strength of Mechitzos. (Traffic is not Mevatel them!)

Question: R. Yochanan does not hold like Chachamim!

(Rabah bar bar Chanah citing R. Yochanan): Had they not locked the doors of Yerushalayim at night, it would have been Reshus ha'Rabim, and one who carried in it would have been liable.

Answer: He says that Chachamim's opinion teaches the strength of Mechitzos, but he himself holds like R. Yehudah.

(Ravin citing R. Yochanan): Steep inclines of Eretz Yisrael are not a Reshus ha'Rabim to be Mechayev one who carries in them, for they are [very] unlike the encampment in the Midbar.

(Beraisa): If Rabim enter through (openings or breaches up to 10 Amos wide on) one side of a Chatzer and leave through another side, it is a Reshus ha'Yachid [regarding Shabbos].

Chachamim would not need to teach this. They say that Rabim do not Mevatel Mechitzos (Pasei Bira'os) even when it is convenient to pass through, all the more so when it is inconvenient!

Rather, R. Yehudah taught this.

Rishonim

Rif and Rosh (Eruvin 2a and 1:8): Tzuras ha'Pesach suffices for Mavoyos Mefulashim to Reshus ha'Rabim. Reshus ha'Rabim itself requires locked doors on both sides, like R. Yochanan taught.

Rambam (Hilchos Shabbos 17:10): If there are two walls in Reshus ha'Rabim and people go between them, one puts a wall on each side, and inside is Reshus ha'Yachid. One need not lock the walls at night, as long as they could be locked.

Rashi (22b DH she'Einan): Inclines of Eretz Yisrael are unlike the encampment in the Midbar. That was smooth. The cloud used to flatten the area.

Rashi (22b DH Ela): R. Yehudah taught the Beraisa. He agrees that Rabim are not Mevatel Mechitzos when it is inconvenient to pass through.

Tosfos (22a DH Kashya): We can say that the one who asked the contradiction thought that R. Yehudah requires three walls for Reshus ha'Yachid mid'Oraisa. Since two walls are proper, Rabim are not Mevatel the third wall.

Tosfos (22b DH Dilma): A Mechitzah not made through man is not so important. Rabanan agree that traffic is Mevatel it.

Tosfos (22b DH Ela): Why didn't the Gemara say that there are two proper walls [in the breached Chatzer]? R. Yehudah surely agrees in such a case! I answer that we must say that all four walls were breached. If only two were breached, what forced the Gemara to say that it is uncomfortable to go through them? Even if it were comfortable to go through them [the area would be considered Reshus ha'Yachid], like the Gemara asked according to Rabanan!

Poskim

Shulchan Aruch (OC 364:2): Reshus ha'Rabim is permitted only through doors. They must be locked at night. Some say that it suffices if it is possible to lock them.

Bi'ur Halachah (DH v'Hu): If they are not locked, and all the more so if there is merely Tzuras ha'Pesach, this opinion says that one is Chayav Chatas [if he carried four Amos there or transferred to Reshus ha'Yachid]. Rabim are Mevatel the Mechitzah. This is like the Rif, Rosh, Semag and other Poskim who brought R. Yochanan's teaching about Yerushalayim l'Halachah. The latter opinion is the Rambam, who holds that even Tzuras ha'Pesach exempts from Chatas. He rules like R. Elazar, that the Rabim are not Mevatel Mechitzos. In any case, the Rambam agrees that mid'Rabanan one needs a door.

Bi'ur Halachah (DH v'Achar): Why is the custom to rely on Tzuras ha'Pesach in Reshus ha'Rabim that is 16 Amos wide and open from one end to the other? We rely on the Rambam, who rules like R. Elazar, that Rabim are not Mevatel Mechitzos. Surely he holds that mid'Oraisa, Tzuras ha'Pesach suffices. Since only an Isur mid'Rabanan remains, we may rely on the opinion that Reshus ha'Rabim depends on 600,000, so Tzuras ha'Pesach suffices for Karmelis. This is not a clear Heter. Most Poskim rule like R. Yochanan, and that we have Reshus ha'Rabim. One may not protest against the masses who are lenient, but a Ba'al Nefesh should be stringent for himself, for it pertains to a Chiyuv Chatas. Also Beis Meir says so.

Aruch ha'Shulchan (1): We hold like Rabanan, who say that Rabim are not Mevatel Mechitzos. Even if they did not lock the doors, Yerushalayim would be only a Karmelis. One may be lenient like the Rambam and Tur to say that the doors need not be locked.

She'alas Ya'avetz (Sof 1:7 DH umi'Kol): May one carry on a frozen river? Boats are not Mevatel its Mechitzos (to make it a Reshus ha'Rabim), for it is unlike the encampment in the Midbar. They did not walk on water or camp on the ice. One cannot camp on the ice, for the sun will melt it (in summer). In such a case Rabim are not Mevatel Mechitzos at all. Muktzeh straw (that people walk on) is Mevatel Mechitzos, for it will stay there on Shabbos. Ice can melt in the middle of Shabbos, and then it is difficult to walk there, and surely Rabim will not walk there! Rather, it is like straw prepared for use, which is not Mevatel Mechitzos, even if the ice is strong.

Chasam Sofer (1:89 DH v'Lihyos): The Taz decreed [to forbid a street open to a frozen river]. Why did the Shach's city ignore this? Perhaps the Taz decreed only in big cities, where they make a crossing over the frozen ice for men, women and children to use without slipping. They would need to walk much further to get to the bridge. This is Mevatel the Mechitzos, because it is convenient to use more than a plank. In small [villages] they do not make crossings. People can slip, and there are ascents and descents, and only light-footed people can cross. It is inconvenient to use. People prefer the bridge. It seems that Shev Yakov holds like this. One may rely on it if the city is surrounded by full walls in the other three directions. She'alas Ya'avetz (Sof 1:7) permits a frozen river, for the sun will melt it (in summer). In such a case Rabim are not Mevatel Mechitzos at all. Even a natural fourth Mechitzah is not Batel through this.

Chasam Sofer: Sefardi Poskim enacted Tzuras ha'Pesach for bridges. They discussed low bridges (even with the level of the city) that they make on boats where the river is deep [and hard to cross, or because] there are rapids. They are Mevatel the Mechitzos of the riverbank. Some bridges are very tall and stand on many pillars. It seems that one ascends 10 Tefachim within four Amos when going from the land onto the bridge. The pillars are 10 Tefachim tall, and make Reshus ha'Yachid. We project the sides of the bridge down to the water through Gud Achis. Fish pass through, but this is not Mevatel the Mechitzos. Even if boats and fishermen pass through, we find that Rabim are not Mevatel Mechitzos of Pasei Bira'os, and all the more so here that it has a roof (the bridge) and not so many pass through. Surely it is Reshus ha'Yachid mid'Oraisa, and one who throws onto it is liable. Also, it seems that the sides of the bridge are walls 10 Tefachim tall. Even if the bridge ascends less than 10 Tefachim within four Amos, it can join to the riverbank to make 10 Tefachim. Any river where boats pass is at least 10 deep. We can project the Mechitzah up. Do not say that Rabim (boats) are Mevatel natural Mechitzos, for here is inconvenient to use.

Aruch ha'Shulchan (363:49): Even if we explain Tosfos simply, that Rabim are Mevatel natural Mechitzos, we do not say so if Rabim pass through only one wall. Tosfos (22a DH Kashya) said so even according to R. Yehudah, and all the more so according to Rabanan. Also the Ba'al ha'Ma'or (6a) says that R. Yochanan holds like R. Yehudah, that Rabim are Mevatel Mechitzos, and two walls make Reshus ha'Yachid. (If not for the doors of Yerushalayim,) there would not be even two Mechitzos, because people go in both directions, and there is not even one wall. This shows that if there would have been one wall without traffic, R. Yehudah would not say that Rabim are Mevatel Mechitzos, and all the more so according to Rabanan.

Aruch ha'Shulchan (50): Rabim are Mevatel Mechitzos only in a place Mefulash to Reshus ha'Rabim, but not if it is Mefulash to Karmelis. Therefore, nowadays it does not apply, for we do not have Reshus ha'Rabim.