Actually, Izzy, property ownership does have some relevance. Along the lines of what I wrote, since people may confuse different kinds of public roads, the Rabbis extended their prohibition even to such places as the common hallway of an apartment building, even though it is fully enclosed.
When I wrote that “there are other requirements as well”, I was referring to “Eruv Chatzeros”, which is needed by a neighborhood even after the wire surrounds it, and is needed by an apartment building even though its own walls surround it.
Izzy, you are correct that ownership is not relevant to whether something is “public domain” or “private domain”, I was merely giving an example of how someone could become confused by thinking that permitted carrying in a Karmelit is the same as a public domain. The meaning of the words “Reshus HaRabim” and “Reshus Hayachid” easily lends itself to confusion on that basis.
And what I’m saying is that the potential confusion is due to the fact that it has no walls, not the lack of private ownership. Were this not the case, a privately owned karmelis would not be included in the g’zeira. (If you have a source for your position let me know - from everything I’ve seen, the similarity is - along the lines of the general rules for r’shuyos - the walled status.)
I must admit that in the course of writing my correction to you, I stopped to ask myself, “Is this confusion really the reason against carrying in the apartment building?” It could well be that I’m mistaken. I had thought that it was all pretty much part of the same package, but I guess I’m going to have to check it out further. Thanks.