The Leeds Logic group
Mathematical logic, a young subject, has developed over the last 30 years into an amalgam of fast-moving disciplines, each with its own sophisticated techniques. These are linked by profound common concerns, around definability, decidability, effectiveness and computability, the nature of the continuum, and foundations. Some branches are highly multidisciplinary and force the researcher to be fully conversant with other fields (e.g. algebra, computer science).
The Logic Group at the University of Leeds is one of the largest and most active worldwide, with a long uninterrupted tradition dating back to 1951, when its founder Martin Löb moved to Leeds. It has an international reputation for research in most of the main areas of mathematical logic - computability theory, model theory, set theory, proof theory, and in applications to algebra, analysis, number theory and theoretical computer science.
More details about the current grants, PhD students, and research interests are on our Research page.
Title: Transfer of NIP in finitely ramified henselian valued fields
By a technique of Jahnke and Simon, itself building on work of Chernikov and Hils, we investigate the transfer of NIP from the residue field to the valued field, in the case of a finitely ramified henselian valued field of mixed characteristic. This relies on understanding the complete theories of such fields, on a certain Ax--Kochen/Ershov principle, and the stable embeddedness of the residue field. This talk will touch on joint work with Franziska Jahnke, and another project additionally with Philip Dittmann.
Title: The space of types with a spectral topology
NOTE time change: 4 pm GMT
Influenced by results in real algebraic geometry, Pillay pointed out in 1988 that the space of types of an o-minimal expansion of a real closed field admits a spectral topology. With this topology, this space is quasi-compact and $T_0$, yet not Hausdorff. Nonetheless, the subspace of all closed points turns out to be quasi-compact and Hausdorff. The purpose of this talk is to present some results on the spectral space of types for o-minimal and more generally NIP theories. This is joint work with Elías Baro and José Fernando.
Title: Small ordered theories with a maximum spectrum of countable models
For theories of totally ordered structures, we consider questions concerning the number of non-isomorphic countable models. The approach is to consider realisations of 1-types, and formulas acting on the set of all realisations of a type.