# Toward Classifying Reducts of the Complex Field

We discuss some recent progress on the model-theoretic problem of classifying the reducts of the complex field (with named parameters and up to interdefinability). The tools we use include Castle’s recent solution of the Restricted Trichotomy Conjecture in characteristic 0 and a generalized sumproduct result from additive combinatorics.

### Affiliation

University of Notre Dame

Chieu-Minh Tran