User blog comment:Upquark11111/An Explanation of Loader's Number/@comment-11227630-20171210002438/@comment-26454151-20171211004323

I found this SE answer that describes every point on the lambda cube. It seems that the main points of interest on the lambda cube are λ→ (STLC), λ2 (System F), λω (System Fω), and λPω (CoC). The answer says that many points of the lambda cube have the same strength as λ→, including λP. It is λ2, which adds the rule $$(\square ,\ast)$$, that makes the jump to second-order arithmetic, and λω makes a further jump to higher-order arithmetic.