12 citations · 33 across the 23 of their papers we have counts for
4 papers · 2 filters
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…
Turing degrees of isomorphism types of geometric objects
Wesley Calvert, Valentina Harizanov, Alexandra Shlapentokh
We initiate the computability-theoretic study of ringed spaces and schemes. In particular, we show that any Turing degree may occur as the least degree of an isomorphic copy of a s…
Definability and Decidability in Infinite Algebraic Extensions
Alexandra Shlapentokh, Carlos Videla
We use a generalization of a construction by Ziegler to show that for any field and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$…