 Gödel delivered the lectures (Gödel 1934) while he was visiting Princeton in the spring of 1934. Already at that time Church, together with his students Kleene and Rosser, had made substantial progress in developing the formal system of function application and abstraction now known as the untyped lambda calculus. This system also provides a means of representing natural numbers as formal terms—i.e., as so-called Church numerals. This leads to a notion of a function being lambda-definable  which is similar in form to (\ref{repfun}). Church’s definition thus also characterize a class \(\mathbf{L}\) of lambda-definable functions which is similar in form to that of \(\mathbf{GR}\). During this period, Kleene demonstrated that a wide range of number theoretic functions were included in \(\mathbf{L}\), in part by showing how it is possible to   implement primitive recursion in the lambda calculus. This ultimately led Church to propose in early 1934 that the lambda-definable functions coincide with those possessing the property which he called “effective  calculability”.[16] 