The UCI research group on Logic and Foundations of Mathematics focuses on set theory and model theory.
Within set theory, there is an emphasis on forcing, large cardinals, inner model theory, fine structure theory, regular and singular cardinal combinatorics, and descriptive set theory. Two aspects of descriptive set theory are studied: the interaction with and application of it in mainstream mathematics, most importantly ergodic theory, as well as its connections to large cardinals, inner models, and determinacy.
Within model theory, there is an emphasis on applications of model theory to other areas of mathematics; such applications often come via nonstandard analysis. There is also an emphasis on model theory of metric structures, e.g. the model theory of operator algebras.
The group is a part of Southern California group in Logic and Foundations, whose members mainly belong to UCLA, Caltech, and UCI. Southern California group was recently awarded the NSF RTG Grant DMS-1044150 which funds several of its new activities.
- Penelope Maddy
- Toby Meadows