Eruv around towns for the purpose of carrying

Question

I was learning the first few chapters of Eyruvin, and I wondering which of the mishnas are the source (or inspiration more likely) for the idea of a string around an area that allows one to carry inside that area.

I would have thought that case of the caravan where they create a "wall" of three strings (1:10) would be the most analogous case, with the issue that as mentioned in the footnotes (it mentioned Eruvin 17b, but don't see where, but I see where it is in the Rambam Hilchot Shabbat 16:12 if I am reading it right) that one cannot enclose an area that has an empty area of size beit satyam (5000 sq amot).

It would seem to me that parks, and many other places probably (parking lots?) would fall under this category.

So in essence I have three questions:

1. Is Eruvin 1:10 the source/inspiration for the eruv around towns that exist today?
2. If so and if the issue of the beit satyam of "utensil-less space" is in the gemara, then how is this issue dealt with?
3. If the issue is not brought up in the Gemara, then where does the Rambam get this idea?

Answer 1

Eruvin 1:10 is actually talking about a different kind of mechitzah, one based on the halachic principle of lavud (where objects within three tefachim of each other are considered joined). So the case there is that they place vertical stakes in the ground, each within three tefachim of the next. (The previous mishnah describes the opposite case - where they string horizontal ropes whose aggregate thickness is more than a tefach, and place them within three tefachim of each other, thus creating a partition ten tefachim tall - the minimum for it to be valid.)

Today's eruvin use instead a series of tzuras hapesach, doorframes (a pair of vertical poles, such as utility poles, and a horizontal crossbeam or wire atop them), which halachically can be considered walls. The concept is mentioned in Eruvin 1:1, and the details - in particular, the idea of using a series of them - in the Gemara ibid. 11a; Rambam deals with it in Hil. Shabbos 16:16.

It should be noted, though, that Rambam would not accept most present-day city eruvin, because he understands the Gemara there to be saying that in any eruv that doesn't use lavud as its operating principle, there must be more filled-in space than open space (e.g., for an eruv whose perimeter is 2 miles, the material for the partitions must have an aggregate width of over one mile). Shulchan Aruch, Orach Chaim 362:10 cites other opinions that this is not necessary, and it is those opinions that those who make and use city eruvin follow. (Some people will not use such eruvin, either because they hold with Rambam's opinion, or because of other halachic and/or meta-halachic considerations.)

Answer 2

In the positive integer number of Eruvin that I've seen, the Eruv excludes uninhabitable and purposeless land (such as cemeteries and bodies of water) from its boundary by encircling that land with another internal set of strings, poles and fences.