Main topics of research
Logics of dependence and independence, team semantics, complexity issues, probabilistic independence logic, modal dependence logic, applications to quantum mechanics, social choice and linguistics.
Non-elementary model theory i.e. study of classes such as homogeneous, excellent, abstract elementary and metric classes. Stability theory. Infinitary logic, especially transfinite Ehrenfeucht-Fraïssé games, non-structure theory, i.e. developing methods for constructing complicated models. Abstract model theory, e.g. generalized quantifiers. Set theoretic model theory, e.g. transfer principles and universality of regular reduced products. Model theory of quantum physics.
Trees and transfinite games, combinatorial properties of uncountable trees, generalized Baire spaces, generalized cardinal invariants, inner models arising from extended logics.
Philosophy of mathematics
Gödel studies, logicality, second order logic, internal categoricity, history of logic, philosophy of set theory.
Finite model theory
Generalized quantifiers on finite models. New methods for establishing non-expressibility results. Descriptive complexity theory. Hierarchy results for finite models.
Other topics include eLearning, logic and analysis, and nonstandard analysis.