2 papers
math.LO2026
On the notion of a patterning property in model theory
Gabriel Day, Scott Mutchnik
Different kinds of definable patterns in the models of a first-order theory, such as the order property, the tree property, or the (-)strict order property, allow us to distingu…
math.LO2025
Results on Colored Tree Properties
Gabriel Day
In this paper, we introduce novel variations on several well-known model-theoretic tree properties, and prove several equivalences to known properties. Motivated by the study of ge…