 Gödel (1934), Alonzo Church (1936a, b) and Alan Turing (1936–7) came up independently with different proposals for an exact mathematical definition of computable functions, and consequently, of decidable sets (of numbers). These proposals, though, all turned out to be equivalent. Turing’s careful conceptual analysis which used fictional and abstract computing machines (nowadays conventionally called “Turing machines”; see the entry on  Turing machines)  was particularly important, as Gödel himself emphasized (see, e.g., Gödel 1963). The equation of the intuitive notion and some of these mathematical explications is often called “The Church-Turing-thesis”. The label “recursive function” has, for historical reasons, been dominant in the logical literature. Consequently, decidable sets are often called “recursive sets”. (See the entries on  computability,  recursive functions and  the Church-Turing thesis.)