 As Gödel’s original approach focused on his specific though very comprehensive system P and its (primitive recursive) extensions, some doubted the generality of Gödel’s results. Alonzo Church, for example, in a letter to Gödel in July 1932, suggested that Gödel’s results would not apply to his system of \(\lambda\)-conversion (the system was later proved to be inconsistent by Kleene and Rosser). Gödel was anxious to generalize his discoveries, and extended the results to a wider class of systems in papers in 1932 and 1934. He also suggested that his methods would be applicable to standard systems of set theory (however, it was only after the satisfactory characterization of decidability and the Church-Turing thesis a few years later that it was possible to give a fully general formulation of the incompleteness theorems (see above); this was first done in Kleene 1936). The eminent set-theorist Ernst Zermelo directed some rather harsh criticism towards Gödel’s work, but the two also corresponded on the topic. Zermelo seems to have had serious difficulties in understanding the relevant concepts and results.