Model theory is a branch of mathematical logic which studies mathematical structures such as graphs, groups, fields etc. by considering what can be said about them in a formal first-order language. It has connections and interactions with many parts of mathematics. Two important, related themes are 'categoricity' and 'stability' (interpreted broadly): the extent to which a structure can be specified in the formal language and the complexity of the collection of subsets of the structure definable in the language. A range of projects in model theory is available related to stable structures, for example on: strongly minimal sets; geometry of forking; amalgamation constructions; higher amalgamation properties; measurable structures. Projects on infinite permutation groups are also available and involve the use of model theortic methods to both construct infinite structrues with ‘large' automorphism groups, and also to study the group-theoretic structure of these automorphism groups.

General information about model theory can be found in the references given here. You can look at my webpage for papers and slides of talks related to my specific interests.

This project is also open to any applicant (home, EU or Overseas) who have their own funding. 

Katrin Tent and Martin Ziegler, ‘A course in Model Theory', Cambridge University Press.

David Marker, 'Model Theory: an introduction' Springer GTM 217.

Bruno Poizat, 'A course in model theory', Springer Universitext.