| 31. | Fundamental results of computability theory show that there are functions that can be precisely defined but are not computable.
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| 32. | BlooP and FlooP can be regarded as models of computation, and have sometimes been used in teaching computability.
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| 33. | The definition of hyperarithmetical sets as \ Delta ^ 1 _ 1 does not directly depend on computability results.
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| 34. | :I don't think he's trying to make a formal analogy between computability and geometry.
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| 35. | Optimization problems themselves are still of interest in computability theory, as well as in fields such as operations research.
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| 36. | The requirement of computability reflects on and contrasts with the approach used in analytic number theory to prove the results.
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| 37. | Computability theory is the part of the theory of computation that deals with what can be computed, in principle.
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| 38. | Stephen Cole Kleene ( 1943 ) presented a proof of G�del's incompleteness theorem using basic results of computability theory.
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| 39. | The same definition of recursive function can be given, in computability theory, by applying Kleene's recursion theorem.
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| 40. | As with the concept of a computable function relative computability can be given equivalent definitions in many different models of computation.
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