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This embedding assumption is the strongest large cardinal axiom that appears in the literature.
The strongest large cardinal axiom in the current literature is the axiom asserting that there is a non-trivial elementary embedding j: L Vλ+1)→ L Vλ+1) such that crit(j)<λ.
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Another important, and much stronger large cardinal notion is supercompactness.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com