 Church’s λ-calculus has its origin in the papers (Church 1932, 1933) and which were intended as a logical foundation for mathematics. It was Church’s conviction at that time that this different formal approach might avoid Gödel incompleteness (Sieg 1997: 177). However, the logical system proposed by Church was proven inconsistent by his two PhD students Stephen C. Kleene and Barkley Rosser and so they started to focus on a subpart of that logic which was basically the λ-calculus. Church, Kleene and Rosser started to λ-define any calculable function they could think of and quite soon Church proposed to define effective calculability in terms of λ-definability. However, it was only after Church, Kleene and Rosser had established that general recursiveness and λ-definability are equivalent that Church announced his thesis publicly and in terms of general recursive functions rather than λ-definability (Davis 1982; Sieg 1997).