The main interests are in set theory and model theory. These subjects have considerable significance in their own right as part of the foundations of mathematics, but their interactions with other areas of mathematics are also important and sometimes surprising. Of particular interest to us are the interactions between set theory, infinite combinatorics and general topology, and between model theory and group theory and algebraic geometry. There are strong links to the Research Group in Algebra and Combinatorics, particularly via David Evans' work on automorphism groups of infinite structures. There are currently three PhD students in the group, and we have an informal working seminar at which we discuss topics of common interest.
Mirna Dzamonja
Set theory and its applications:
Combinatorial set theory and independence results. Interaction of
set theory with other fields of mathematics, most particularly
set-theoretic model theory, topology and measure theory.
Large cardinals. Recent works
include various aspects of the universality problem, that is, the
existence of the universal object in a given class of objects, and
some aspects of the interaction of forcing with large cardinal methods.
David Evans
Model Theory and Infinite Permutation Groups:
Automorphism groups of first-order structures. In particular, questions on
aleph-zero categorical structures and their automorphism
groups; covers of aleph-zero categorical structures.
Algebraic model theory, particularly the model theory of groups.
Stability theory, its generalisations and
geometries associated with regular types. Applications in algebra.
Model
Theory and Infinite Permutation Groups at UEA
Set Theory and
Applications of Set Theory at UEA
Graduate
Brochure