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.
Location: MALL 1
Title: O-minimal tame set-theoretic topology
We give a positive answer in the o-minimal setting to a conjecture in set-theoretic topology and explore similar open problems in topology from the point of view of o-minimality.
The British Postgraduate Model Theory Conference (BPGMTC) 2023 is a Model Theory conference organised entirely by PhD students running from 18 to 20 January 2023. The conference is open to PhD students and early career researchers, one of its main goals being to bring together young researchers interested in model theory from the UK and abroad. The BPGMTC has been a longstanding tradition in the UK, this year the University of Leeds is proud to be holding the thirteenth edition of BPGMTC!
Title: Forcing over choiceless models
Forcing over models of ZF set theory without the axiom of choice has been studied in particular for L(ℝ) in work of Steel, Van Wesep, Woodin and more recently Larson and Zapletal. However, the axiom of choice can fail in much stronger ways than in L(ℝ). For example, in Gitik’s celebrated model all uncountable cardinals are singular. Since virtually all known forcing techniques fail in this situation, it is interesting to understand what forcing does to such models. We develop a toolbox for forcing over arbitrary choiceless models. We further introduce very strong absoluteness principles and show their relation with Gitik’s model. This is joint work with Daisuke Ikegami and in part with W. Hugh Woodin.