Gödel’s Incompleteness Theorems reveal the fundamental complexity of arithmetic, both in negative sense, i.e., the undecidability of the theory of the natural numbers, but also in positive sense that first-order language of fields is far more expressive than one might think. The structures born from the interaction of logic and number theory/arithmetic geometry are at the center of extensive and intensive study at the frontier of computability theory, model theory, number theory and arithmetic geometry.
Among the topics at the core of the program, the focus will be on:
- Decidability and computability, e.g. Hilbert Tenth Problem over arithmetically
significant domains. - Definability, e.g., definability of valuations, definability in arithmetic geometry.
- Computability, e.g., effectiveness and complexity of countable structures.
Link to Trimester Program website
Scientific Organizers:
- Valentina Harizanov (George Washington University)
- Philipp Hieronymi (University of Bonn)
- Jennifer Park (Ohio State University)
- Florian Pop (University of Pennsylvania)
- Alexandra Shlapentokh (East Carolina University)
Trimester Program Events:
- Introductory School "Definability, Decidability, and Computability" (September 8 – 12, 2025)
- Workshop "Definability in Number Theory and Arithmetic Geometry" (October 20 – 24, 2025)
- Conference "Definability and Computability" (December 8 – 12, 2025)
In addition to the activities listed above, there will be a weekly seminar with speakers from the participants and/or short-term visitors as well as possibly ad-hoc talks on “hot topics”.