There is a long-standing dispute amongst posqim - To 600K or to NOT 600K? Or in English, does a R'shut Harabbim require 600,000 people traversing it or not in order to be so construed halachically speaking?
It's highly unlikely that I will resolve this 800+ year dispute online, but I will offer a radical paradigm shift. So stay tuned, and get ready to fasten your safety belts!
I will be going down two parallel paths.
1. The status of desert
2. The issue WRT 600K
There are many sources to start with. I choose to begin with SA Orach Hayyim 345. [If you own a Mishna Brura it's the beginning of Vol. IV]
There the Four Domains are listed, defined and illustrated [The Number *4* itself is a curious anomaly. There is at least a 5th domain - viz. Qarpeif!] But since the SA follows a Braitto in TB Shabbos 6 and keys off of it, therefore it stays with its opening Intro that there are 4 domains....
Note: In 345:7 the Mechabeir takes his ambiguous stance on the 600K Prerequisite. Dear Readers, you are invited to research from that point.
Meanwhile I would like to post what I *Don't* see! And that is the status of a Midbar or Desert. What is most curious is the TB. Shab. 6 *DOES* have midbar! So what does the SA indicate from silence?
Furthermore, [Working backwards] the Tur in 345 also is silent WRT Midbar
But the grand-daddy of the Halachic Codes is not ambiguous at all! The Rambam in Hilchot Shabbat 14:1 mentions deserts . And there he unequivocally declares it to be the very First in a list of R'Shut Harabbim [RhR] cases!
A The Talmud in several Braittot on Shabbat 6 mentions the status of Midbar
B The Rambam states it's a RhR
C The Tur AND SA omit Midbar [maybe it deserted them?]
D The SA is ambivalent WRT the 600K issue
Shabbat 6, the Braittot, the question of the Talmud, and Abbaye's answer