In the summer of 1942 he submitted his Habilitation thesis Provability and nonprovability of restricted transfinite induction in elementary number theory to Göttingen and, on the award of the degree, he became entitled to teach in universities.
Sa tag-init ng 1942 na isinumite niya ang kanyang Habilitation tesis Provability at nonprovability ng restricted transfinite pagtatalaga sa tungkulin sa elementarya bilang teorya sa Gottingen at, sa award ng degree, siya ay naging karapat-dapat na magturo sa unibersidad.