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==Name==

==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 (Soare 1996) 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.<ref>[[Mathscinet]] searches for the titles like "computably enumerable" and "c.e." show that many papers have been published with this terminology as well as with the other one.</ref> 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<ref>Lance Fortnow, "[https://blog.computationalcomplexity.org/2004/02/is-it-recursive-computable-or.html Is it Recursive, Computable or Decidable?],"  2004-2-15, accessed 2018-3-22.</ref> and Simpson.<ref>[[Steve Simpson (mathematician)|Stephen G. Simpson]], "[http://www.cs.nyu.edu/pipermail/fom/1998-August/001993.html What is computability theory?]," FOM email list, 1998-8-24, accessed 2006-1-9.</ref>

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 (Soare 1996) 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.<ref>[[Mathscinet]] searches for the titles like "computably enumerable" and "c.e." show that many papers have been published with this terminology as well as with the other one.</ref> 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<ref>Lance Fortnow, "[https://blog.computationalcomplexity.org/2004/02/is-it-recursive-computable-or.html Is it Recursive, Computable or Decidable?],"  2004-2-15, accessed 2018-3-22.</ref> and Simpson.<ref>[[Steve Simpson (mathematician)|Stephen G. Simpson]], "[http://www.cs.nyu.edu/pipermail/fom/1998-August/001993.html What is computability theory?]," FOM email list, 1998-8-24, accessed 2006-1-9.</ref>