DU Mathsoc is proud to present this week’s talk on model theory – delivered by Mathsoc’s own Brian Tyrrell, our current librarian! In Brian’s own words, “Model theory is a field of mathematics that lies in the intersection of mathematical logic and abstract algebra. The fundamental objects of study are models, which can be applied to branches like group theory, graph theory and algebraic geometry, however their properties can be studied in their own right. Using first order and infinitary logic we can write sentences that can describe these structures up to isomorphism – the project I did over the summer at the University of Notre Dame studies the characteristics of these special sentences (called Scott sentences) and in this talk I will present some of the conditions that are needed for the Scott sentence of a countable model to have uncountable models.