Classical computability theory originated with the seminal work of Gödel, Church, Turing, Kleene and Post in the 1930's, and includes a wide spectrum of topics, such as the theory of reducibilities and their degree structures, computably enumerable sets and their automorphisms, subrecursive hierarchy classifications, computable structures, and complexity theory relating to the preceding.
There are still very many open questions, both of a technical nature, concerning extensions of what is known about the Turing degrees and their context in the enumeration degrees, and similar questions for other natural reducibility degree structures, and less well-defined questions concerning the scope of relevance of such work.
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