Not really. Goedel's incompleteness theorem says that no consistent set of axioms can prove all true statements. Moreover, once you take a few unprovable, but t

Not really. Goedel's incompleteness theorem says that no consistent set of axioms can prove all true statements. Moreover, once you take a few unprovable, but true, things and add them to you axioms, there will still be things that are true that you cannot prove. This means that you're not going to find two mutually exclusive sets of axioms that, between the two of them, can prove any and all true things. This suggests to me that there's not a Library of Babel of mathematical universes, it's more or less one big universe, with a lot of black holes.