Was the dream of the crumbling city Limbo? Or was it just a Level 4 dream?
To Fischer, it was a limbo because he was shot and evidently taken hostage by Mal into that world, in order to lure Cobb in. To Cobb and Ariadne, although it is the same dream space, you can take it as a level 4 dream because they used machine to go through. In addition, when Aridane and Fischer left the dream via death and they did not end up in "limbo". This suggested they are in fact already in limbo and death was the way out. Cobb, on the other hand, had to be "kicked" from the dream via explosion at the snow fort. Therefore the crumbling city was both a limbo and a level 4 dream.
It is indeed Limbo. We gather this because it is the same world that Cobb and Mal spent 50 years in previously. Cobb not only describes how he and Mal built the world, but remembers the world distinctly.
However many consider it to be a fourth level of the dream world. I think this is because we once again see Cobb wash up on the shore of Limbo when he meets Saito. However I believe that because Cobb initially entered Limbo on his own volition when he died in either Limbo (from Mal's stab) or level 1 (by drowning) he re-entered Limbo in an area created by Saito to live in.
(Addition to the original answer:) I support the notion that this is Limbo even though Cobb and Ariadne enter it through the machine. I don't recall anyone saying that you have to die to enter Limbo, i.e. dying in a dream to be the only way to get there. Mal and Cobb previously probably also entered it by using the dream machine.
Another argument against this being Limbo is that Ariadne and Fischer go up to the next dream level when they die (by falling off the building). This however may be the normal way of leaving Limbo; waking up directly into reality (like Cobb and Saito did) probably only happens if the other dream levels do not exist anymore as the dreamers have woken up already.
Alternative alternative answer.
Fischer didn't die, he was left in a coma-like state. A defibrillator is used for life-threatening conditions, not for dead patients (see Wikipedia link below). He was just unconscious, i.e. dreaming. Therefore, he didn't go to Limbo, but descended to another dream level: Level 4. Cobb and Ariadne join Fischer in his dream using the dream machine - you can tell Fischer is doing the dreaming, and all three are connected, by the lightning Ariadne sees in the sky of Level 4: this comes from the defibrillator shocks experienced by Fischer, which is transmitted in lightning form into his dream, much like the music or water is transmitted. OR Cobbs is doing the dreaming, and the shock is transmitted to his Level 3 body along the wires - they're all connected, remember. This would let Cobbs design and create the "Limbo" landscape.
Ariadne and Fischer leave Level 4 because there is a kick in the level above, just like all the other non-Limbo levels. Falling off the building is a redundant plot device. In any case, it would be the falling sensation that provides the kick, and not the impact (i.e. they didn't need to kill themselves, it was a regular dream level). But there's no Level 5, and no one sleeping on Level 4, so why the kicks on Level 4? Maybe they need to die after all, maybe they are in Limbo! Oh dear. Or maybe it's just inconsistent.
It is not Limbo just because it looks like the Limbo Cobb left. Cobb could be using his memories of Limbo to create an imperfect replica, with (what we are explicitly told is) an imperfect replica of Mal inside.
Most likely Cobb drowns in the van on Level 1 because he does not / cannot heed the kicks and wake up (why the other team members don't try harder to release him is a mystery!). Satio also dies on Level 1, the level where the wound was inflicted, even if we see him collapse on Level 3. Satio dies before Cobb, so he enters Limbo earlier, which explains his old age when Cobb is finally washed up on the shores of Limbo. If Level 4 is indeed Limbo, then Cobb would have entered it earlier than Satio, and would be the older man. He is not.
And remember, Limbo involves delirium, loss of grip on reality etc. Cobb might avoid some of this (he eventually avoided it with Mal the first time), but Ariadne? Fischer? Wouldn't they be totally disorientated if this was Limbo proper? Like Cobb washed up on the beach?
Interestingly, if Limbo is deep down, then you can't just go from Reality to Limbo, so Cobb and Mal would have gone up just one dream level after the train crash. Mal was right, they never woke up. Perhaps they never could, Limbo was the best they could ever hope for.
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