In logic, mathematics and computer science, especially metalogic and computability theory, an effective method[1] or effective procedure is a procedure for solving a problem by any intuitively 'effective' means from a specific class.
In order for a method to be called effective, it must be considered with respect to a class of problems.
Adding this requirement reduces the set of classes for which there is an effective method.
Several independent efforts to give a formal characterization of effective calculability led to a variety of proposed definitions (general recursive functions, Turing machines, λ-calculus) that later were shown to be equivalent.
The Church–Turing thesis states that the two notions coincide: any number-theoretic function that is effectively calculable is recursively computable.