12 citations · 33 across the 23 of their papers we have counts for
12 papers · 1 filter
Computability in infinite Galois theory and algorithmically random algebraic fields
Wesley Calvert, Valentina Harizanov, Alexandra Shlapentokh
We introduce a notion of algorithmic randomness for algebraic fields. We prove the existence of a continuum of algebraic extensions of that are random according to our…
A Computable Functor From Graphs to Fields
Russell Miller, Bjorn Poonen, Hans Schoutens +1
We construct a fully faithful functor from the category of graphs to the category of fields. Using this functor, we resolve a longstanding open problem in computable model theory,…
On decidable algebraic fields
Moshe Jarden, Alexandra Shlapentokh
We prove the following propositions. Theorem 1: Let be a subfield of a fixed algebraic closure $\tilde \Q$ of $\Q$ whose existential elementary theory is decidable (resp. primi…
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…