John Brunner's novel, "The Infinitive of Go" is a story about teleporting devices based on a "posting" principle affecting living objects in the process of "posting" - the author describes it in terms of "congruent spaces". In particular, sentient beings end up affecting the destination they reach because the computers operating the posting devices, based on "transfinite mathematics", take into account the postee's thoughts and desires at the moment of transfer, shuttling him/her to a universe closest to his/her desires (in addition to matching the physical elements of the two universes).

The author ends up postulating that physical reality "is of order aleph four, perhaps aleph five". The one reason he may have needed this transfinite element in the story is due to an assumption about a continuously branching Reality as in Everett's many-worlds theory (I don't know if that autuomatically gets you up to aleph 1 or 2 - perhaps someone has done a calculation on this. He appears to have assumed the truth of the continuum hypothesis as well). A couple of additional alephs have been thrown in as "levels that our consciousness does not even perceive. At one point, he mentions that the infinity of such universes is larger than the infinity of curves. The final line of the novel hints at some transcendent gods observing these myriad universes...