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On Kalimullin pairs
Computability - The Journal of the Assosiation
We study Kalimullin pairs, a definable class (of pairs) of enumeration degrees that has been used to give first-order definitions of other important classes and relations, including the enumeration jump and the total enumeration degrees. We show that the global definition of Kalimullin pairs is also valid in the local structure of the enumeration degrees, giving a simpler local definition than was previously known. We prove that the typical enumeration degree is not half of a nontrivialdoi:10.3233/com-150046 fatcat:ycbsja6hxrgwzpfgsdg7c64244