3 papers
math.LO2026
On Cohesive Products of Fields
Rumen Dimitrov, Valentina Harizanov, Henry J. Klatt +1
We develop the foundations of effective ultraproducts of fields and their Galois groups using the methods of computability theory. These computability-theoretic analogs of ultrapro…
math.LO2026
sp-Homogeneous Linear Orderings
Wesley Calvert, Douglas Cenzer, David Gonzalez +2
We study linear orderings expanded by functions for successor and predecessor. The successor and predecessor on linear orderings capture the relatively intrinsically computably enu…
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…