Eruvin, Chapter Five, Mishnah 6. This mishnah deals with the status of making eruvei chatzeiros and shitufei mevo'os for an entire city. The halachah is that a city made up of many alleyways, with courtyards opening off each alleyway, can be made into a single unit - through one shituf, one partnership formed over food - and thereby it will be permitted to carry throughout the entire city.
A city belonging to an individual and a city belonging to the public:
A city belonging to an individual - a city owned by a private person, who rents out places within his private city to various people to live in.
A city belonging to the public - a general public city, owned by the community.
The halachic difference between them: in a city belonging to an individual, one may make shitufei mevo'os and eruvei chatzeiros for the entire city, thereby permitting carrying throughout all of it.
In a city belonging to the public, however, since it resembles a public domain - after all, it is a public area - the Sages said that there must be a distinguishing feature, something that sets it apart from a public domain. The majority of the city may make shitufei mevo'os and carry throughout the whole area, but an area must be left aside that is not included in the general shituf permitting the carrying. This area must be separate and distinct: it may make its own shitufei mevo'os and carry within itself, but one may not transfer from one to the other. This separation is the distinguishing feature - a noticeable distinction that shows this is not a public domain.
The novel point of the mishnah - a city whose status changed:
The mishnah deals with a city that was originally one type of city and afterward became the other type:
"Ir shel yachid v'na'aseh shel rabim - me'arvin es kulah" - a city belonging to an individual, in which one may make a shituf mevo'os for the whole city so that everyone can carry throughout it, and afterward it became a city belonging to the public and its ownership and status changed - it retains its original law, and one may make an eruv for all of it so that everyone can carry within it.
"Shel rabim v'na'aseh shel yachid - ein me'arvin es kulah" - here too the city retains its original status, except that its original status was that of a city belonging to the public, a public city in which a separate area must be set aside, from which one may not carry to the rest of the area; rather it makes a shituf mevo'os of its own.
The measure of that separate area:
The mishnah continues: "Ela im kein asah chutzah lah k'ir chadashah sheb'Yehudah, sheyeish bah chamishim diurin" - "Chadashah" here is not a description but the name of a city in Yehudah. That is, unless one makes outside the general area a separate section containing fifty residents - fifty people living in that area. An area large enough to have a population of fifty is required, and if it does, it is a separate area in its own right: they make their own shitufei mevo'os but do not join with the rest of the city. This is the view of Rabbi Yehudah regarding the measure of the area that must be separated off in a city belonging to the public, or in a city belonging to the public that became one belonging to an individual.
"Rabbi Shimon omer: shalosh chatzeiros shel shnei batim" - Rabbi Shimon has a different measure, and it is not based on the number of people but on the layout: three courtyards, each courtyard containing at least two houses - this is a sufficient area to serve as the separate area in a city belonging to the public, while the rest of the city makes its shitufei mevo'os together.
In practice, the halachah is that even a single courtyard containing one house is enough to serve as the separate area.
In summary: We learned that a single eruv can be made for an entire city, and that there is a distinction between a city belonging to an individual, for which an eruv may be made for all of it, and a city belonging to the public, which resembles a public domain and requires a distinguishing feature by separating off an area not included in the general eruv. A city whose status changed retains its original law, and regarding the measure of the separate area Rabbi Yehudah and Rabbi Shimon disagree: Rabbi Yehudah says fifty residents, and Rabbi Shimon says three courtyards of two houses each, while the halachah is that even one courtyard containing one house suffices.