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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.

Upcoming events

120 Years of Choice

In 1904 Ernst Zermelo published his paper, Beweis, daß jede Menge wohlgeordnet werden kann, proving that every set can be well-ordered. This prompted the efforts to axiomatise and clarify the foundations of set theory and mathematics. This year, we are celebrating 120 years of choice and order.

There will be a tutorial session, 16 lectures, and 2 poster sessions.

Registration to the conference is open until 20 June 2024. Please consider registering early so we can better estimate the number of participants!

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Leeds Computability Days 2024: Computability, Reverse Mathematics, and Topology

Registration for LCD 2024 is required. The fee is £40. The deadline is 21 June 2024.

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Dianthe Basak (Paris)

Location: MALL 1
Title: Continuous Actions of Monoids, a New Perspective on Large Cardinals

The standard "symmetric models" approach to building models of the failure of the axiom of choice relies on the action of non-discrete topological groups on a universe of sets (either sets-with-atoms or a boolean valued model of names). A new approach interprets large cardinal axioms as positing the action of non-discrete topological monoids on the universe of sets (a model of names, a model with atoms, or even $V$ itself). By understanding such actions, one can reinterpret (and reprove) the Kunen inconsistency theorem as a symmetric model theorem, as well as interpreting a version of the HOD conjecture in a natural way. The talk will attempt to place such techniques in their natural context and highlight some applications.

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