# Main topics of research

#### Model theory

Research topics in model theory include

- non-elementary model theory i.e. study of classes like homogeneous, excellent, abstract elementary and metric classes.
- infinitary logic, especially transfinite Ehrenfeucht-Fraïssé games are studied and in connection with these games the group studies non-structure theory, i.e. develops methods for constructing complicated models. Problems in this topic are often problems on trees, which has led the group to study combinatorial properties of uncountable trees.
- abstract model theory, e.g. generalized quantifiers.
- set theoretic model theory, e.g. transfer principles and universality of regular reduced products.

#### Set theory

Topics in set theory include various aspects of trees and transfinite games, usually arising from model theoretic questions. A new interest is generalized cardinal invariants.

#### Finite model theory

In finite model theory the group has started a vigorous investigation of generalized quantifiers on finite models. New methods for establishing non-expressibility results have been developed with a keen eye on the possibility of obtaining new hierarchy results for finite models.

#### Logic and analysis

In the topic of logic and analysis the group has studied

- first-order definability and expressibility in rings whose elements are complex analytic functions defined in a common domain, combining methods of classical complex analysis with those of logic and set theory.
- There is also some work done on Brownian motion with the help of nonstandard analysis.

#### Other topics

Other topics include eLearning, dependence logic and philosophy of mathematics.