We position Turing’s result regarding the undecidability of the halting problem as a result about programs rather than machines. The mere requirement that a program of a certain kind must solve the halting problem for all programs of that kind leads to a contradiction in the case of a recent unsolvability result regarding the halting problem for programs. In this paper, we investigate this auto...

We investigate which effectively presented abelian p-groups are isomorphic relative to the halting problem. The standard approach to this and similar questions uses the notion of ∆2-categoricity (to be defined). We partially reduce the description of ∆ 0 2-categorical p-groups of Ulm type 1 to the analogous problem for equivalence structures. Using this reduction, we solve to a problem left ope...

Most of the existing work in real number computation theory concentrates on complexity issues rather than computability aspects. Though some natural problems like deciding membership in the Mandelbrot set or in the set of rational numbers are known to be undecidable in the Blum-Shub-Smale (BSS) model of computation over the reals, there has not been much work on different degrees of undecidabil...