My course was an introduction to some topics related to circular phenomena, especially matters close to non-wellfounded sets, circularity in computer programs, and coalgebra. The work on computer programs was a self-contained introduction to the subject using 1#. The theme of the other topics is best found in the 'conceptual comparison chart' that can be found in some of the sets of lecture slides, the chart that compares algebraic and coalgebraic concepts along with least and greatest fixed points, etc.

The course was given at the European Summer School in Logic, Language, and Information held in Opole, Poland, August 13-17, 2012. It consisted of five 90 minute lectures and was attended by 50-75 people, I think.

The lectures were partly delivered as you see them in the slides. But at many points I changed the presentation to a more conversational style. This was most evident in the second lecture, where many people in the class advocated for a solution to the Hypergame Paradox that was much more like the one involving the Foundation Axiom. In addition, the third lecture was partly a lecture/demo on 1#, and it was my intention to have everyone try to write circular programs after only a few minutes of introduction. This wasn't quite possible, but I think many people did come away with the basic ideas. In any case, I have changed the slides to make them more readable for people who did not attend the course. But more can be done in this respect, I'm sure.

Circular phenomena: a catalog to motivate the course

Here are the slides.

Hypergame and its treatment using the Foundation and Anti-Foundation Axioms

Here are the slides.

Self-writing computer programs

Here are the slides.

Here is a link to the 1# interpreter.

Here is a link to the web text on this topic.

Category theoretic concepts related to circular phenomena

Here is an the set of slides from Thursday. These go beyond what I covered Thursday, and so the first part of Friday's lecture is also included.

The final set of slides from the course represented a lecture that was too fast for people who had not seen category theory before.