Research in the Natural Sciences and Mathematics
Dr. Natasha Dobrinen
Assistant Professor, Department of Mathematics
Dr. Dobrinen's research interests mainly fall under the broad category of Logic and Foundations of Mathematics. Specifically, her focus is on research in Set Theory and Boolean Algebras, overlapping with Recursion Theory and Measure Theory. Dr. Dobrinen's research has been motivated by a formerly unsolved problem of von Neumann regarding an algebraic characterization of measure algebras. In that vein, she characterized many generalized distributive laws in Boolean algebras in terms of infinite length games for two players. More recently, Dr. Dobrinen has been investigating strong combinatorial properties and their consistency strengths in the axiomatic system of set theory. These include co-stationarity of the ground model in an extension universe and the tree property. In addition to classifying other useful combinatorial properties in terms of their consistency strengths, she is currently working on classifications of partial orderings of small infinite cardinality in terms of embeddings which preserve certain combinatorial properties.
Learn more about Dr. Dobrinen's research by visiting http://www.math.du.edu/dobrinen
