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