Please note that the list below only shows forthcoming events, which may not include regular events that have not yet been entered for the forthcoming term. Please see the past events page for a list of all seminar series that the department has on offer.

 

Past events in this series


Thu, 22 May 2025

17:00 - 18:00
L3

Axioms of Quantum Mechanics in the light of Continuous Model Theory​

Boris Zilber
(University of Oxford)
Abstract

I am going to start by reviewing axioms of quantum mechanics, which in fact give a description of a Hilbert space. I will argue that the language that Dirac and his followers developed is that of continuous logic and the form of axiomatisation is that of "algebraic logic" in the sense of A. Tarski's cylindric algebras. In fact, Hilbert spaces can be seen as a continuous model theory version of cylindric algebras.

Thu, 29 May 2025
17:00
L3

The hierarchy of consistency strengths for membership in a computably enumerable set

Joel David Hamkins
(University of Notre Dame)
Abstract
For a given computably enumerable set W, consider the spectrum of assertions of the form n ∈ W. If W is c.e. but not computably decidable, it is easy to see that many of these statements will be independent of PA, for otherwise we could decide W by searching for proofs of n ∉ W. In this work, we investigate the possible hierarchies of consistency strengths that arise. For example, there is a c.e. set Q for which the consistency strengths of the assertions n ∈ Q are linearly ordered like the rational line. More generally, I shall prove that every computable preorder relation on the natural numbers is realized exactly as the hierarchy of consistency strength for the membership statements n∈W of some computably enumerable set W. After this, we shall consider the c.e. preorder relations. This is joint work with Atticus Stonestrom.
Thu, 05 Jun 2025
17:00
L3

TBA

Antoine Sedillot
(Universität Regensburg)