This is not the BioShock we know. Linked only thematically to the first two titles, BioShock Infinite promises a breath of fresh air - seriously, the other two were set underwater - for veterans, and an open entry point for new players.
It is set in the breakaway city-state of Columbia, the year is 1912, and the world is getting used to the idea of American exceptionalism.
Forget about the city upon a hill, though - this one floats above them all. Up there in the clouds, the citizens have taken their ideals to uncomfortable extremes, under the leadership of a bent prophet. They pray to Washington, Jefferson and Franklin for guidance and then use their wisdom to persecute minorities and perpetuate filthy levels of sexism, all protected by police who wouldn't have been out of place under Hitler.
It is your bad luck to be the prophesied "false shepherd". A veteran of the US Cavalry, Booker DeWitt is tasked with recovering the "lamb" - a mysterious young woman named Elizabeth - and delivering her in order to clear a debt. You might understand how that might upset the locals. You can deal with them in this first-person shooter using a range of firearms, supernatural abilities, and a clever tool called the Sky-Hook. That allows you to ride overhead cables in a flying fox-like fashion and butcher enemies with brutal efficiency.
Elizabeth is a disapproving accomplice, albeit willing, and she's a great character: a triumph of voice acting, animation and design who out-Disneys cinema's favourite princesses. Mechanically, she is a supporting character whose abilities include opening rifts in space and time to supply Booker with items and tricks, but she provides a blessedly liberal counterpoint to all the happy fascists.