Generalized logics and inner models
Oct. 26, 2026 – Oct. 30, 2026
This workshop, sponsored by AIM and the NSF, will focus on connections between two kinds of inner models for Set Theory. The first is the well studied family of extender models, i.e. fine-structural models designed to contain large cardinals by incorporating extender sequences. The second is the new family of inner models, e.g. the aa-model, arising from extended logics, which has the potential to bring completely new insights into set theory. The area of properties of the new inner models as well as connections between the two kinds of inner models abounds in open problems and the forthcoming workshop provides an ideal opportunity for trying to solve them.
The main topics of the workshop are:
- Connections between the two kinds of inner models.
- The role of the HOD of the Chang Plus model in this picture.
- Fine structure for the new inner models.
- Large cardinals in the new inner models.
This event will be run as an AIM-style workshop. Participants will be invited to suggest open problems and questions before the workshop begins, and these will be posted on the workshop website. These include specific problems on which there is hope of making some progress during the workshop, as well as more ambitious problems which may influence the future activity of the field. Lectures at the workshop will be focused on familiarizing the participants with the background material leading up to specific problems, and the schedule will include discussion and parallel working sessions.
For more information email workshops@aimath.org