Natasha Dobrinen has been awarded a three-year NSF Research Grant for her study, "Ramsey Theory, Set Theory, and Tukey Order." The grant is Dobrinen's second on the subject, which develops the theory of structures at the interface of three fields of mathematics. Ramsey theory focuses on the conditions under which order must appear. Set theory deals with the formal properties of sets as units without regard to the nature of their individual constituents, serving as an axiomatic foundation for all of mathematics similarly to the way that geometry is developed from a collection of postulates. Tukey order is a means of comparing relative strengths of different structures. The project finds connections between and strengthens these areas of mathematics, leading to new theory and a better understanding of mathematical structures.