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PvP stands for player-vs-player combat. The game includes a multiplayer mode which allows the player to engage other player controlled characters. It's been confirmed that sandbox mode will allow PvP in Beta, with features like arenas and special PvP modes being developed for post-release.
What's been suggested by developers for organized PvP areas are pre-generated asteroids with a score keeping system. This has been confirmed not to be released with the game, but as a later update.