Recursion theory

Name

The field of mathematical logic dealing with computability and its generalizations has been called "recursion theory" since its early days. Robert I. Soare, a prominent researcher in the field, has proposed that the field should be called "computability theory" instead. He argues that Turing's terminology using the word "computable" is more natural and more widely understood than the terminology using the word "recursive" introduced by Kleene. Many contemporary researchers have begun to use this alternate terminology. These researchers also use terminology such as partial computable function and computably enumerable (c.e.) set instead of partial recursive function and recursively enumerable (r.e.) set. Not all researchers have been convinced, however, as explained by Fortnow and Simpson. Some commentators argue that both the names recursion theory and computability theory fail to convey the fact that most of the objects studied in computability theory are not computable.