Karen Lange, Wellesley College
Classification via effective lists
'Classifying' a natural collection of structures is a common goal in mathematics. Providing a classification can mean different things, e.g., identifying a set of invariants that settle the isomorphism problem or creating a list of all structures of a given kind without repetition of isomorphism type. Here we discuss recent work on classifications of the latter kind from the perspective of computable structure theory. We’ll consider natural classes of computable structures such as vector spaces, equivalence relations, algebraic fields, and trees to better understand the nuances of classification via effective lists and its relationship to other forms of classification in this setting.