Lectures between 18.11. - 21.11.2025, DMS building (lecture rooms M3, M5 and M6)

Itai Ben-Yaacov

Continuous first-order logic and metric structures

Tue 18.11. 15:00-14:00 (M3)
Wed 19.11. 14:00-15:00 (M5)
Thu 20.11. 11:00-12:00 (M6)
Fri 21.11. 14:00-15:00 (M5)

Abstract: In this series of lectures I will cover as much as possible the basic notions and tools pertaining to continuous first-order logic as a logical framework for studying metric structures.
I shall attempt to cover mostly points where there are some "surprises" when compared with  classical logic.

- Syntax and semantics.   Compactness.   Types and type spaces.
- Approximate homogeneity (and approximate saturation) in separable structures.
- Definable sets.
- Type isolation, omitting types, Ryll-Nardzewski characterisation of separable categoricity.

If time allows, I might also discuss other, related topics, such as the recently very much studied affine logic.