Achim jung

On cartesian closed categories of domains

7 mai 2015

Abstract: This is a topic that I thought I had finished working on more than 20 years ago but through some novel ideas of Jean Goubault-Larrecq I have recently come back to it and been able to show some new results.

The problem concerns finding a cartesian closed category of (Scott) domains which is also closed under the probabilistic powerdomain construction. As of today, the problem is open.

Jean's new idea was to extend Scott's notion of "continuity" and he was indeed able to show that there is a larger category of "quasicontinuous domains" which supports the Jones-Plotkin probabilistic powerdomain. Our new result shows that - unfortunately - quasicontinuous domains will not provide any new cartesian closed categories.

In my talk I will give the background to the open problem outlined above and explain what we know and what we don't know about the structures involved.