- University of Gothenburg
- Faculty of Humanities
- Department of Philosophy, Linguistics and Theory of Science
- Research
- Research Areas
- Logic
- The Lindström Lectures
- The Lindström Lectures 2018

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# The Lindström Lectures 2018

## Public Lecture of Michael Rathjen

### Progressions of theories and slow consistency

## Research Lecture of Michael Rathjen

### Bounds for the strength of the graph minor and the immersion theorem

The Department of Philosophy, Linguistics and Theory of Science at the University of Gothenburg launched a lecture series in 2013 to celebrate the singular achievements of **Pelle Lindström**, former professor of logic at the department (in the photo).

Annually, a distinguished logician is invited to deliver a general lecture to the public, and a specialized presentation at the logic seminar.

We are proud to announce that the 2018 Lindström Lectures will be delivered by **Michael Rathjen**.

Michael Rathjen is Professor of Pure Mathematics at University of Leeds. He obtained his Ph.D. (1988) and Habilitation (1992) at University of Münster. Rathjen is renown for his fundamental contributions to Proof Theory, especially cut elimination for infinitary proof systems, ordinal analysis of impredicative theories and calibration of set-existence strength of combinatorial principles. He has also carried out penetrating investigations in intuitionistic and constructive mathematics, including Martin-Löf type theory.

- Monday, 11th June, 2018
- 18:00–20:00 at Eklandagatan 86, room TBA.

Abstract: The fact that “natural” theories, i.e. theories which have something like an ‘idea’ to them, are almost always linearly ordered with regard to logical strength has been called one of the great mysteries of the foundation of mathematics. Using paradoxical methods, e.g. self-reference Rosser-style, one can distill theories with incomparable logical strengths and show that the degree structure of logical strengths is dense in that between two theories S<T one can always find a third Q such that S<Q<T. But are there ‘natural’ examples of such phenomena? We also know how to produce a stronger theory by adding the consistency of the theory. Can we get a stronger theory by adding something weaker than consistency that is still “natural”? These and other questions will be broached in the talk.

- Wednesday, 13th June, 2018
- 10:00–12:00 at Eklandagatan 86, room TBA.

Abstract: The graph minor theorem, GM, is arguably the most important theorem of graph theory. The strength of GM exceeds that of the standard classification systems of RM known as the “big five”. The plan is to survey the current knowledge about the strength of GM and other Kruskal-like principles, presenting lower and upper bounds.