 Related to the question of solvability or unsolvability of problems is that of the reducibility or non-reducibility of one problem to another. Thus, if problem \(P_1\) has been reduced to problem \(P_2\), a solution of \(P_2\) immediately yields a solution of \(P_1\), while if \(P_1\) is proved to be unsolvable, \(P_2\) must also be unsolvable. For unsolvable problems the concept of reducibility leads to the concept of degree of unsolvability, two unsolvable problems being of the same degree of unsolvability if each is reducible to the other, one of lower degree of unsolvability than another if it is reducible to the other, but that other is not reducible to it, of incomparable degrees of unsolvability if neither is reducible to the other. A primary problem in the theory of recursively enumerable sets is the problem of determining the degrees of unsolvability of the unsolvable decision problems thereof. We shall early see that for such problems there is certainly a highest degree of unsolvability. Our whole development largely centers on the single question of whether there is, among these problems, a lower degree of unsolvability than that, or whether they are all of the same degree of unsolvability. (Post 1944, 289)