  The Princeton logician Alonzo Church had slightly outpaced Turing in finding a satisfactory definition of what he called ‘effective calculability.’ Church's definition required the logical formalism of the lambda-calculus. This meant that from the outset Turing's achievement merged with and superseded the formulation of Church's Thesis, namely the assertion that the lambda-calculus formalism correctly embodied the concept of effective process or method. Very rapidly it was shown that the mathematical scope of Turing computability coincided with Church's definition (and also with the scope of the general recursive functions defined by Gödel). Turing wrote his own statement (Turing 1939, p. 166) of the conclusions that had been reached in 1938; it is in the Ph.D. thesis that he wrote under Church's supervision, and so this statement is the nearest we have to a joint statement of the ‘Church-Turing thesis’: