Just thought I would add there are time travel paradoxes that the Novikov self consistency principle does not prevent. Basically, Novikov considers spacetime as whole, and states there is one state of every event. Time travel is possible, but the single state of everything avoids many paradoxes. Thus, it is perfectly ok for grandfather to meet time traveling grandson who claims to be from the future. But there would not be some alternate grandfather to whom this never happened. Instead, this just is part of grandfather's history, and grandson might have heard about this before they left.
Note that some interpretations Novikov principle imply no significant material body can follow a CTC (but they could follow an open time loop instead). These argue that, e.g. a decaying lump of uranium following an actual CTC creates a Novikov problem because when the CTC closes, you have changed the past because the number of decayed atoms must suddenly change (with any nontrivial material body, its exact collection of atoms and states is continually changing - it is just easier to argue with uranium decay). With a 'near CTC', there is no problem you have e.g. a future state of the uranium body coming out of a wormhole next to its earlier state. Both then age from there, and at some point the 'younger one' is sent back to through the wormhole to be come the older one. Note, the distant past and distant future have only one state of the body.
However, Novikov does not prevent so called information paradoxes. My favorite is that a time traveler visits Shakespeare with a copy of "Julius Caesar", while Shakespeare has not yet written this play. She gives him the copy she brought back. Shakespeare likes it, transcribes it, burns the copy. There is no Novikov violation in this sequence - this is just the way it "always was". But the play has no author whatsoever!
