I agree with the other guy, its probably related to an i nfinite  number of parallel universes or timelines. Given the new information thats what I am going for and its probably the way Columbia was constructed, by getting things from alternate universe and all taken through the filter of early 1900's. That or it just relates the feeling of being unbound by nations and land and that  Columbia can do anything because of it. I cant wait to play this game regardless of the title.

It's in the sky. 

I agree with the other guy, its probably related to an i nfinite  number of parallel universes or timelines. Given the new information thats what I am going for and its probably the way Columbia was constructed, by getting things from alternate universe and all taken through the filter of early 1900's. That or it just relates the feeling of being unbound by nations and land and that  Columbia can do anything because of it. I cant wait to play this game regardless of the title.

Maybe infinite space, like more space than just indoor levels.

I think INFINITE reffers to the city in the sky. Like people's attitude in this game is "we can build anything, we can go anywhere, the sky's the limit". And that's why it's called Infinite.

Infinite possibilities.  Infinite imagination.  Infinite universes.  Infinite I don't know and it probably doesn't matter.

Infinite Bioshocks.

It's infinite because that way, no one can make an awful sequel and just stick 2 on the end because the name BioShock Infinite 2 is Final Fantasy levels of stupid. It's basically the way the Xbox 360 was named that to make sure the number was bigger than what Sony had, it's the same thing here.

Infinite universes, of course. And perhaps the ability to travel between them