2025 Lindström Lectures: Jouko Väänänen
published: 2025-09-03
event dates:
2025-11-17
–
2025-11-18
On 17–18 November 2025, University of Gothenburg will host the 2025 edition of its annual Lindström Lectures. The Lindström Lectures is a distinguished lecture series initiated in 2013 celebrating the memory of Per (Pelle) Lindström, former (and first) professor in logic at the University of Gothenburg.
The 2025 edition of The Lindström Lectures will be delivered 17–18 November 2025 by Jouko Väänänen, Professor of Mathematics at the University of Helsinki and the Institute for Logic, Language and Computation at the University of Amsterdam. See the webpage of the 2025 edition for more information.
Public Lindström Lecture
Monday, 17 November 2025 at 18:00
On the Logic of Dependence
Abstract
Dependence and independence concepts are ubiquitous in natural science, social science, humanities as well as in everyday life. The sentences “I park on this side of the road depending only on the day of the week” and “the time of descent is independent of the weight of the object” are examples of this. The question arises, do these concepts possess enough exactness for us to investigate their logic? There is currently a whole literature on this topic. It is the purpose of this talk to give a non-technical overview of this area of logic.
Research Lindström Lecture
Tuesday, 17 November 2025 at 10:00
In Search of New Lindström Theorems
Abstract
The combination of Löwenheim-Skolem Theorem and Compactness Theorem limits the expressive power of a logic to that of first order logic. This maximality principle is the famous Lindström Theorem for first order logic. It reveals that first order logic is at an optimal point of balance: by adding expressive power to it one necessarily loses model-theoretic properties. Soon after Lindström’s result, the question was raised, whether there are other logics at a similar point of equilibrium. More precisely: are there strict strengthenings of first order logic satisfying a Lindström-type characterization? Despite the naturality of this question, it remained unanswered, until recently.
In 2012 Saharon Shelah offered a solution to this problem in the form of a new infinitary logic. It has a Lindström-type characterization in terms of model-theoretic properties combining weak forms of Compactness and a Löwenheim-Skolem type property. In all known cases, a proof of a Lindström-type characterization automatically gives a proof of Craig Interpolation. This is the case for Shelah’s logic, too. There is, however, one aspect where Shelah’s logic seems to be rather weak: the syntax. The logic is derived from a game, in the sense that a sentence is, by definition, a class of structures, closed under a certain Ehrenfeucht-Fraïssé type of a game. This results in the absence of a syntax defined in such a way that the set of all formulas could be obtained by closing the set of atomic formulas under negation, conjunction, quantifiers, and possibly other logical operations. The lack of syntax complicates further study of it and logics in its neighborhood. In the present talk, we address the general question of deriving a syntax from a game, and the more localized question of finding a syntax for Shelah’s logic. Partial answers are provided to both questions. This is joint work with Andres Villaveces and Siiri Kivimäki.