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The jump is definable in the structure of the degrees of unsolvability

1990
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Bulletin of the American Mathematical Society
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Recursion theory deals with computability on the natural numbers. A function ƒ from N to N is computable (or recursive) if it can be calculated by some program on a Turing machine, or equivalently on any other general purpose computer. A major topic of interest, introduced in Post [23], is the notion of relative difficulty of computation. A function ƒ is computable relative to a function g if after equipping the machine with a black box subroutine that provides the values of g, there is a

doi:10.1090/s0273-0979-1990-15923-3
fatcat:d3g7bx5i6neufhcr5b5i32okie