Computable structure theory explores the computational properties of mathematical structures, such as groups. As a subfield of computability theory, this area frequently draws on methods from model theory—particularly infinitary model theory—and algebra. Much of this research is motivated by Scott’s Isomorphism Theorem, which states that by extending first-order logic to include countably infinite conjunctions and disjunctions, every countable structure can be described up to isomorphism (among countable structures) by a single sentence known as a Scott sentence.

In addition to scholarly work in computable structure theory, Rachael Alvir maintains an active interest in the philosophy of mathematics and logic, with a particular focus on Gödel’s incompleteness theorems.