A naive extension is an informal concept cited by Sbiis Saibian,^{[1]} used to refer to a method of extending a googological system in a way that is obvious and adds no new insight. Specifically, a naive extension of a googological system takes a concept iterated inside that system and lazily applies it again. The Aarex function is an example, which is a naive extension of the xi function and \(f_{\varphi^{CK}(\omega,0)}(0)\).

\(U_2(a)\) is defined similiar to U(a), but with 2nd order array notation.

Even though this function grows quite a bit faster, as the growth rate in FGH is doubled, it isn't enough for being prevented from being called a naive extension.