On the expressive power of quantifiers in continuous logic

Itaï Ben Yaacov (1, 2)

1 ICJ - Institut Camille Jordan
2 AGL - Algèbre, géométrie, logique

In this short note we compare the expressive power of real-valued continuous logic (or just continuous logic, in recent literature) with that of compact-valued continuous logic, proposed by Chang and Keisler. We conclude that the two logics have the same expressive power, and moreover, that this remains true if we replace the plethora of potential quantifiers of compact-valued logic with a single "primordial" one.

Keywords: Continuous logic; quantifier; Vietoris topology

Domains: Logic [math.LO]

Itaï Ben Yaacov. On the expressive power of quantifiers in continuous logic. 2022. ⟨hal-03712958⟩