Main topics of research
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.
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 include eLearning, dependence logic and philosophy of mathematics.