The title seems apt actually. I think 'universe' here refers to the concept of a set so large that it is closed under all set theoretic operations and since mathematical operations reduce to set theoretic operations (in the usual foundation scheme) one can start with some elements in this universe set and perform any arbitrary manipulation and the output will still be inside this set. http://en.wikipedia.org/wiki/Grothendieck_universe Inter-universal presumably refers to geometrical statements which hold across different such universes. At least, that's my understanding. The paper is well beyond my knowledge.