Idea. Not very clever and it's sooooooo unlikely don't shoot me down just seemed cool but what if Columbia was a simulation using one of the computers in Rapture like Lambs big console thing and Booker is someone trapped in it and elizabeth was another person trapped in and he's trying to get her out and the sumulation is called Operation Infinite or something?
as i said unliklely but could be cool
That's not such a bad idea. Maybe it's some sort of propaganda simulation Ryan hadrigged up. Columbia is the polar opposite of Rapture so it wouldn't be a stretch. Booker and Elizabeth could be stuck in the simulation too since they were forgotten after New Year's Eve when Rapture went to hell.
I have an even more unlikely theory though! Booker is actually some sort of malfunctioningrobot and he sees Columbia abnormally. It sounds farfetched, but as we all know, Jack from Bioshock 1 had "something" that made his life a lie. Just like someone posted earlier in this topic, the gameplay would reveal what makes this a Bioshock game and Booker could have a sort of "Something" like Jack had.