# Mittag-Leffler objects in definable categories of modules

## Philipp Rothmaler

### The City University of New York

Definable categories are classes of modules closed under direct product, direct limit, and pure submodule. These play an important role in the theory of modules as they are in bijection with the closed sets of the Ziegler spectrum (and thus with the product closed complete theories of modules). Mittag-Leffler objects for such categories (some sort of generalized atomic module) will be introduced and a necessary and sufficient condition in terms of generators and generalized relations will be given for them to exist.

Philipp Rothmaler is a professor of mathematics at the CUNY Graduate Center and at Bronx Community College, working in mathematical logic and especially model theory. He is the author of the highly regarded book, Introduction to Model Theory.