3 papers
math.NT2025
First-order definitions of rings of integral functions over algebraic extensions of function fields and undecidability
Alexandra Shlapentokh, Caleb Springer
In this paper, we study questions of definability and decidability for infinite algebraic extensions of and their subrings of -integral fun…
math.LO2024
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…
math.NT2024
Defining using unit groups
Barry Mazur, Karl Rubin, Alexandra Shlapentokh
We consider first-order definability and decidability questions over rings of integers of algebraic extensions of $\Q$, paying attention to the uniformity of definitions. The unifo…