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NBG set theory proves nothing additional about sets relative to ZFC. MK set theory, on the other hand, is stronger, meaning it should prove statements about sets that NBG and ZFC don't.

Are there some natural examples of statements only about sets provable in MK, but not ZFC or NBG? (aka, not just "Con(ZFC) in some Godel numbering")

Likewise, is there a simple way to augment ZFC with an additional axiom so that MK is now a non-conservative extension that proves exactly the same things about sets?

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