 So, why definability? The motivation was made clear for instance by Bernstein’s “Die Theorie der reellen Zahlen” (1905a), where Cantor’s continuum hypothesis was claimed to be settled in the positive. He criticized the so called “Dirichlet notion” of arbitrary function and stated that it is possible to give a foundation to the continuum using only computable reals, i.e., reals possessing an explicit “formation law” (“Bildungsgesetz”).