You can't play downloaded PS3 games on PS4, though. Unless they're one of the few cross-play games, like Sound Shapes, Flower, etc.
This is the correct answer. DG has said everything correctly so far. Thanks. I just found out this stuff last night after talking to someone at Sony. My PS3 was basically stolen yesterday so I called them to see if they could close out all my stuff and hopefully trace any IP it was connected to (they couldn't do the IP thing). So, looks like I'll be getting a PS4 sooner than thought, lol. I'll probably pick up another PS3 if I can't get mine back so I can play GT.