The axiom is undecidable in ZFC, unlike the full axiom, which contradicts the Axiom of Choice; it follows from certain large cardinal axioms, such as the existence of infinitely many Woodin cardinals.
The axiom is undecidable in ZFC. This is unlike the full axiom. The full axiom contradicts the Axiom of Choice. It follows from certain large cardinal axioms. This is such as the existence of infinitely many Woodin cardinals.