Usually means: Study of what's algorithmically solvable.
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We found 9 dictionaries that define the word computability theory:

General (3 matching dictionaries)
  1. computability theory: Wiktionary
  2. computability theory: Dictionary.com
  3. Computability theory (computation), Computability theory (computer science), Computability theory: Wikipedia, the Free Encyclopedia

Business (2 matching dictionaries)
  1. Computability theory: Legal dictionary
  2. BusinessDictionary.com (No longer online)

Computing (2 matching dictionaries)
  1. computability theory: Free On-line Dictionary of Computing
  2. computability theory: Encyclopedia

Medicine (1 matching dictionary)
  1. online medical dictionary (No longer online)

Science (1 matching dictionary)
  1. FOLDOP - Free On Line Dictionary Of Philosophy (No longer online)

Definitions from Wiktionary (computability theory)

noun:  (logic) Recursion theory.
noun:  (computer science) The branch of the theory of computation that studies which problems are computationally solvable using different models.

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