This page lists potential PhD projects in logic, set theory and model theory, offered by faculty members of the School of Mathematics. For further details of the School's research in this area, please see the Pure Mathematics Research Group page. For further information about an individual project, please contact the listed supervisor. For information about submitting an application, please see our Research Degrees page.

Set Theory and Connections with Other Subjects Set Theory and Connections with Other Subjects

Supervisor: Prof Mirna Džamonja

I am happy to supervise a broad range of projects in set theory and related areas. Concrete suggestions range from problems in Banach space theory to those in the theory of iterations and large cardinals. Specific questions that have interested me recently include combinatorics at the successor of a singular cardinal, uncountable variants of the Fraïsse construction and universality of Banach spaces.

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For further information, please contact Prof Mirna Džamonja.

Model Theory Model Theory

Supervisor: Dr Jonathan Kirby

We can offer a range of topics in pure model theory, and applications of model theory to number theory. Particular interests include amalgamation constructions and their associated geometries, stability theory in an abstract setting, and the model theory of exponentiation. There are strong connections between model theory and Diophantine geometry, including recent progress on the Zilber-Pink conjecture by Jonathan Pila and others. There are both analytic methods (using the model theory of o-minimality) and algebraic methods (based on Zilber's ideas around exponentiation). We can also offer suitable projects in this area. Any interested student is invited to contact Dr Jonathan Kirby to discuss an application.

High Forcing Axioms High Forcing Axioms

Supervisor: Dr David Aspero

Forcing axioms are principles occurring naturally in set theory. These principles assert that some initial segment of the universe is saturated, is some well-defined sense, relative to some large number of generic extensions of it. Models of these principles are naturally produced by suitable iterated forcing extensions. Due to technical reasons, most classical forcing axioms pertain the initial segment of the universe known as H2). The techniques for producing similar forcing axioms for H3) and higher up are new or yet to be developed. In this project we focus on the study of these high forcing axioms, and more specifically on their combinatorial consequences and on their consistency.

I am also happy to supervise projects in set theory with different flavours and in and other related areas. My interests are mostly in forcing, forcing axioms, infinite combinatorics, set-theoretic topology, large cardinals, definability issues, and interconnections between these areas.

For further details, please contact Dr David Aspero.