User blog comment:Upquark11111/An Explanation of Loader's Number/@comment-11227630-20171210002438/@comment-26454151-20171210030039

David Moews cites a paper that shows that second-order lambda calculi (i.e. with parametric polymorphism) are able to express fast growing functions. Specifically, the paper cited shows how to code $$f_{\varepsilon _0}$$ in System F, and David Moews claims the same method can be trivially extended to code faster growing functions. System F is a weaker lambda calculus than λPω and appears on the lambda cube as λ2. I don't feel like paying money to get access to the paper, so I don't know how to code anything above $$f_{\varepsilon _0}$$.