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math.LO2023
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.LO2023
Cohesive Powers of Structures
Valentina Harizanov, Keshav Srinivasan
A cohesive power of a structure is an effective analog of the classical ultrapower of a structure. We start with a computable structure, and consider its countable ultrapower over…