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Kleene's recursion theorem: Quiz


Question 1: ________, which are used in lambda calculus for the same purpose as the first recursion theorem.
Type systemSimply typed lambda calculusFixed point combinatorAnonymous function

Question 2: The second recursion theorem is closely related to definitions of computable functions using ________.
Mathematical logicRecursionMathematicsRecursion (computer science)

Question 3: Consider the recursion equations for the ________ function f:
Gamma functionPrime numberExponentiationFactorial

Question 4: The two recursion theorems can be applied to construct fixed points of certain operations on ________, to generate quines, and to construct functions defined via recursive definitions.
Computable functionHalting problemComputability theoryTuring machine

Question 5: This restriction is similar to the restriction to continuous operators in the Kleene fixed-point theorem of ________.
Binary relationPartially ordered setOrder theoryLattice (order)

Question 6: Arslanov's completeness criterion states that the only recursively enumerable ________ that computes a fixed point free function is 0′, the degree of the halting problem.
Turing degreeMathematical logicComputability theoryAlan Turing

Question 7: ________, where another least fixed point theorem is used for the same purpose as the first recursion theorem.
Functional programmingDenotational semanticsActor modelLambda calculus

Question 8: In ________, Kleene's recursion theorems are a pair of fundamental results about the application of computable functions to their own descriptions.
First-order logicHilary PutnamComputability theoryMathematical logic


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