Of the things which may be just theoretically examined as being 'true' or not, likely the one that i personally regard as more or less not possible, is to have a subset at the same time being larger than a carrying set of it. The prospect just echoes chaos. At least some fundamental sense of progression either has to exist (eg set/subset/subsubset etc), or alternatively there could just be One thing there and no sets or subsets.
But i am not seeing how there can be many things around, and some subsets including their sets. This actually seems ominous. (i don't mean setting special axioms so that you can have a symmetry system that supposedly allows for a subset to contain its set. I mean it (to put it more intensely, although not having to be that precise: ) if the microcosm collapses in smaller parts of it to the 'same' set which the macrocosm is.
(a story by Borges contains vaguely a similar idea, of a spiral or helix string of universes that repeat and connect back to each other at the start/end-- 'The route to Al-Motashim').
But i am not seeing how there can be many things around, and some subsets including their sets. This actually seems ominous. (i don't mean setting special axioms so that you can have a symmetry system that supposedly allows for a subset to contain its set. I mean it (to put it more intensely, although not having to be that precise: ) if the microcosm collapses in smaller parts of it to the 'same' set which the macrocosm is.
(a story by Borges contains vaguely a similar idea, of a spiral or helix string of universes that repeat and connect back to each other at the start/end-- 'The route to Al-Motashim').