It is very near the bottom of Kanamori's chart. The very bottom of the chart is the level of a (strongly) inaccessible cardinals, which is the smallest large cardinal axiom. Right above the inaccessibles in the chart are the α-inaccessible cardinals. It turns out that the Universe Axiom (UA) is strictly weaker than the existence of a 2-inaccessible cardinal. In fact, κ is 2-inaccessible if and only if V<sub>κ</sub> ⊧ ZFC + UA. Specifically, a cardinal κ is: * *0-inaccessible* iff κ is regular, * *1-inaccessible* iff κ is a regular strong limit of 0-inaccessibles, * *2-inaccessible* iff κ is a regular strong limit of 1-inaccessibles, * etc. So an inaccessible cardinal is exactly the same as a 1-inaccessible cardinal, which are also precisely the cardinals κ such that V<sub>κ</sub> ⊧ ZFC. If κ is 2-inaccessible, then there are unboundedly many inaccessibles λ < κ. These are inaccessible in V<sub>κ</sub> too, which is why V<sub>κ</sub> satisfies UA.