If every B-preserving isomorphism between two worlds must be A-preserving, then if any B-preserving isomorphisms exist between two worlds, at least one of them must be A-preserving.
Possible ways the universe could be or could have been—like alternate realities with different facts and events.
isomorphism(The strongest structural correspondence between two many-sorted structures.)
An embedding between structures in which all defining maps are bijections.
necessary and sufficient conditions(in philosophical analysis)
A 'necessary' condition is something that must be true for something else to happen; a 'sufficient' condition is something that guarantees it will happen. This phrase describes what must be true (and what's enough) for a definition to apply.
It is easy to see that strong global supervenience entails intermediate global supervenience, which in turn entails weak global supervenience. If every B-preserving isomorphism between two worlds must itself be A-preserving, then if there are any B-preserving isomorphisms between two worlds at all, at least one of them must be A-preserving. So, strong global supervenience entails intermediate. And if at least one of any existing B-preserving isomorphisms between two worlds must itself be A-prese