ps3 to 4. should I switch?

[monochromicorn]

I have a playstation 3 and just got a playstation four. If I BUY a copy for PS4 can I still play on my PS3? For example, I work at home and I want to have my PS4 downstairs and my PS3 upstairs so I can craft while I am at work. As long as I am only logged into my account on one of the stations at a time, I could play on either station if I bought a PS4 license? I just wanna be sure before I plunk down another $40.

Thanks!

its cheaper to transfer the license and re-buy the game for ps3. the transfer is free, iv done it, and its cheaper for ps3