He had examined simplified methods of deriving the paradoxes (such as those of Richard and Russell) in systems of logic which are inconsistent, and had also developed a method of introducing into combinatory logic undefined notions of generality, such as quantification or formal implication, in such a way that a consistency theorem like that of Church and Rosser could still be derived.
Niya napagmasdan pinadali pamamaraan ng panggagaling ang paradoxes (tulad ng mga ng Richard at Russell) sa sistema ng lohika na kung saan ay paiba-iba, at nagkaroon din ng isang paraan ng nagpapakilala sa combinatory lohika malabo notions ng pahayag, tulad ng dami o pormal na implikasyon, sa tulad ng isang paraan na ang isang pagbabago teorama tulad na ng Iglesia at Rosser ay pa rin nagmula.