Welcome to the course Stone Duality: Connecting Algebra and Topology via Logic! It is given at the 37th European Summer School for Logic, Language, and Information (ESSLLI 2026) in Prague, Czechia.
Course description
This course is an introduction to Stone duality, which is an exciting area of logic and neighboring disciplines like math, computer science, and philosophy. Stone’s theorem says that certain algebras (Boolean algebras) are in a precise sense equivalent to certain topological spaces (zero-dimensional compact Hausdorff spaces). The underlying idea is that the two seemingly different perspectives—the algebraic one and the spatial one—are really two sides of the same coin:
- formulas of a logic vs. its models,
- open sets of a space vs. its points,
- observable properties of a computational process vs. its denotation
- propositions vs. possible worlds.
After an interdisciplinary motivation, the course will introduce the mathematical theory, followed by applications. The goal is to show both the conceptual and technical potential of dualities by translating between the two sides and thus using their respective advantages.
Practical information
- The course takes place during the first week of ESSLLI 2026 (August 3–7, 2026), from 09:00 to 10:30 in room C206.
- You can contact me with questions, comments, and feedback at Levin [dot] Hornischer [at] lmu [dot] de.
Materials
- You can find the slides for the lecture here:
esslli26.pdf. Note the slides will still be updated as the course progresses. - I also have given a full semester course on Stone duality, on which the present course is based. You can find the lecture notes of that course here.
- Both in the slides and in the lecture notes, you find many references to excellent further material on duality theory.
Preliminary schedule
| Lecture | Topic |
|---|---|
| 1 | Introduction and motivation |
| 2 | Boolean algebras |
| 3 | Stone spaces |
| 4 | Stone’s theorem (statement) |
| 5 | Proof and applications |