Gemara

(Mishnah - R. Meir): We give [room for] a Karfef to a city [before measuring the Techum];

Chachamim say, we give a Karfef only between two cities;

If when we give 70 and two thirds Amos to each city, these areas overlap, the cities are considered like one.

(Mishnah - Chachamim): We give a Karfef only...

(Rav Huna): Two Karfifos are given for two cities;

(Chiya bar Rav): We give only one Karfef.

Question (Seifa): If when we give 70 and two thirds to each city, they overlap, they are considered like one city.

Answer: R. Meir taught the Seifa.

46a (R. Yehoshua ben Levi): The Halachah follows R. Yochanan ben Nuri. (One who was asleep at the start of Shabbos gets 2000 Amos in every direction.)

R. Yehoshua ben Levi also taught that the Halachah follows the lenient opinion in Eruvin.

He needed to teach the Klal (general rule), and also to rule like R. Yochanan ben Nuri, to teach that we follow the lenient opinion in Eruvin, even when an individual argues with a Rabim.

32b (Rava): The Mishnah discusses a tree outside the Ibur. Within the Ibur, even if the Eruv is above 10, it is valid.

Nedarim 56b (Mishnah): If one vowed from a city, he may enter its Techum, but not its Ibur (the surrounding 70 Amos and two thirds).

(R. Yochanan): We learn from "when Yehoshua was in Yericho..."

This cannot mean that he was in the city itself. The city was closed off! Rather, he was in its Ibur.

Rishonim

Rif (16b) and Rosh (5:3): Rav Huna says that we give two Karfifos for two cities. Chiya bar Rav says that we give only one. One who vows from a city is permitted in its Techum, but forbidden in Iburah.

Rambam (Hilchos Shabbos 28:1): If a residential house is within 70 Amos and two thirds of the city, it joins with it, and it is considered part of it. We measure 2000 Amos from this house.

Rosh (5:3): A Beraisa (Sukah 3a) says that a house less than four by four Amos cannot be an Ibur between two cities. This is difficult. R. Meir gives a Karfef to each city even without a house. Rabanan give one or two Karfifos, according to Chiya bar Rav and Rav Huna respectively, even without a house! If there is more than 141 and a third Amos between two cities, and therefore we need a house to join them, why did it mention two cities? It should have said that we do not make it an Ibur for a city, for also one city can make shacks to [extend the city to enable one to] go as far as desired (21a)! Due to this question, the Rashbam changed the text to say 'cannot be an Ibur for a city.' The Yerushalmi connotes like this. It says 'we do not make an Ibur for a city.' I.e. we do not connect it to the city. R. Tam defends our text. The Beraisa means that the house does not get the law of an Ibur between two cities, for Rabanan do not give a Karfef to one city. If the house were four by four, it would be considered a [second] city, and we would give one Karfef to the city and a second Karfef for the house according to Rav Huna, and according to Chiya bar Rav, just one Karfef for both of them. Rabanan did not mean that Karfef applies only to two cities. The same applies to a city and a house. Through shacks, we can extend a city.

Rosh: R. Tam rules like Rav Huna, for he was greater than Chiya bar Rav. Also, the Amora'im answer for Rav Huna and discuss his opinion. Further, even Chiya bar Rav would agree that we give two Karfifos to two cities, for he holds that the Stam Seifa is R. Meir. There is an argument, and then a Stam Mishnah, so the Halachah follows the Stam. Also Maharam says that the Halachah follows R. Meir, since R. Yehoshua ben Levi said that the Halachah follows the lenient opinion in Eruvin, even when an individual argues with a Rabim. He brought another proof from 32b. Rava distinguished between a tree inside the Ibur and one outside the Ibur.

Poskim

Shulchan Aruch (OC 398:5): If a residential house is within 70 Amos and two thirds of the city, it joins with it, and it is considered part of it. We measure 2000 Amos from this house.

Beis Yosef (DH u'Le'acher): The Rosh and Mordechai bring that Maharam rules like R. Meir. However, it seems that the Rambam rules like Chachamim. Also the Rif brought the Mishnah Stam. This connotes that he rules like Chachamim, for they are the majority. However, perhaps he relied on what he wrote (12b) that the Halachah follows the lenient opinion in Eruvin, even when an individual argues with a Rabim. We can prove that he rules like Chachamim, for he brought the argument of Rav Huna and Chiya bar Rav, which is according to Chachamim. According to R. Meir, surely we give two Karfifos. However, the Rif brought that one who vows from a city may not enter Iburah. This implies that we give a Karfef even to one city, for it was taught Stam! However, perhaps he brought it merely to bring an Asmachta for Ibur from the verse, but Chachamim give a Karfef only to two cities. Since there is not an important Shi'ur between them, they are like one. Even though regarding vows, the Ibur is considered like the city, vows depend on the way people speak. Alternatively, the Rif brought it to teach that the Tana forbids entering an Ibur between two cities, just like here, that we give a Karfef only to two cities.

Magen Avraham (5): A residential house helps even if people do not live there.

Kaf ha'Chayim (24): A house does not help if it is Arai, i.e. people do not live there on a fixed basis due to thieves or flooding from rain. Where there are no thieves, it is counted. A shack helps even if it is not four by four.

Rema: Some do not begin measuring from this house. Rather, we extend a string across the width of the city even with the house, and distance 70 Amos and two thirds from there and begin. The same applies whenever we measure. It seems to me that we are lenient.

Gra (DH v'Yesh): This is like R. Meir, for the Halachah follows the lenient opinion in Eruvin. Also, Rava holds like R. Meir. The Rosh brings so from Maharam, who learns from 46b. He understands that the Halachah follows the lenient opinion in Eruvin, even when an individual argues with a Rabim, always. (The Tur rules like this.) This is difficult. If so, he (the Tur) should rule like every individual [who is lenient], e.g. R. Shimon allows 15 Amos past the Techum, and so rules the Rashba there!

Note: The Tur (405) rules unlike R. Shimon, but the Rashba (52b and Avodas ha'Kodesh Beis Nesivos 5:13) rules like R. Shimon.

Gra (according to Damesek Eliezer): Also in other places [the Tur rules like the Rabim, even when they are stringent]. Also, the Gemara (46a) connotes unlike this [that we are lenient like an individual against a Rabim. If so, the Gemara should have concluded 'this teaches that the Halachah follows the lenient opinion, even against a Rabim'! Rather, the Halachah also follows the Rabim [even] in Eruvin. The Rif rules like this. The Rif wrote the Mishnah in which R. Meir and Chachamim argue, and did not rule like R. Meir. Also the Rosh's proof from Rava is invalid. Also, a Stam Mishnah (60a) says that an Eruv in the Ibur of a city does nothing. This connotes that the Halachah follows R. Meir. However, Rashi said that there is a house inside the Ibur [so this does not prove that the Halachah follows R. Meir - PF]. Rashi said similarly on 32b.] The Gemara connotes like the Rambam [who discussed an Eruv in a place that joins with the city. He did not simply write 'in Iburah.' This is like Rashi], that here (46a), the Halachah follows R. Yochanan ben Nuri. Also the Rif and other Poskim wrote [that the Halachah follows Chachamim].

Mishnah Berurah (21): We give 70 Amos and two thirds before measuring the Techum even when there is no house. The first opinion measures from the wall, and gives Karfifos only for two cities.

Bi'ur Halachah (DH v'Chen): The Rosh and Mordechai bring like this from Maharam, and the Rashba agrees. The Mechaber holds like the Rambam, Semag, Ritva and Bartenura. We do not protest against one who is lenient, especially since the Rema is lenient. However, the Rema brings from the Tur that when there is a house within 70 and two thirds, we give from there another 70 and two thirds before measuring the Techum. This is difficult. The Rashba says that the Ra'avad disagrees, and did not bring another opinion. The Ritva says that even those who give a Karfef to one city, if there is a house there, give only 70 and two thirds from the city. Surely one must be concerned for their opinion, since the first opinion does not give a Karfef at all. The Gra holds that the first opinion is primary.