Infinite, but the number of players is limited to one. The third BioShock game doesn't include multiplayer, as confirmed by series creator Ken Levine on Twitter.
There's been speculation about multiplayer features in Infinite, with reports of modes cut in conjunction with staff changes at developer Irrational Games. BioShock 2 introduced competitive multiplayer to the series, a divisive move given the acclaim for the first game as a story-driven, single-player experience.
With BioShock Infinite due in a few months, fans are already looking ahead to the series' future on the next batch of consoles. One Twitter user asked Levine if he'd prefer to work on a new IP, or would he be taking BioShock to next-gen platforms. Levine's reply? "Not sure." Maybe he's stuck on how he'll mathematically number the next one.