Strongly Minimal Sets in Continuous Logic

Abstract: Continuous logic is a generalization of first-order logic suited to studying structures with a real-valued metric. There is a natural generalization of the notion of strongly minimal sets to continuous logic, and, while they do not play quite the same role in characterizing theories categorical in uncountable cardinalities, they are interesting in their own right. After developing some of the basic machinery of strongly minimal sets in continuous logic, we will characterize the essentially continuous strongly minimal theories, i.e. those which do not interpret an infinite discrete structure, and we will leverage this into a precise characterization of the essentially continuous strongly minimal groups.

logic

Audience: researchers in the topic

Online logic seminar

Series comments: Description: Seminar on all areas of logic