35 citations · 86 across the 22 of their papers we have counts for
5 papers · 1 filter
The Distance Function on a Computable Graph
Wesley Calvert, Russell Miller, Jennifer Chubb Reimann
We apply the techniques of computable model theory to the distance function of a graph. This task leads us to adapt the definitions of several truth-table reducibilities so that th…
Computable Categoricity for Algebraic Fields with Splitting Algorithms
Russell Miller, Alexandra Shlapentokh
A computably presented algebraic field has a \emph{splitting algorithm} if it is decidable which polynomials in are irreducible there. We prove that such a field is comp…
Categoricity Properties for Computable Algebraic Fields
Denis Hirschfeldt, Ken Kramer, Russell Miller +1
We examine categoricity issues for computable algebraic fields. We give a structural criterion for relative computable categoricity of these fields, and use it to construct a field…
The hierarchy of equivalence relations on the natural numbers under computable reducibility
Samuel Coskey, Joel David Hamkins, Russell Miller
The notion of computable reducibility between equivalence relations on the natural numbers provides a natural computable analogue of Borel reducibility. We investigate the computab…
Noncomputable functions in the Blum-Shub-Smale model
Wesley Calvert, Ken Kramer, Russell Miller
Working in the Blum-Shub-Smale model of computation on the real numbers, we answer several questions of Meer and Ziegler. First, we show that, for each natural number d, an oracle…