Interpolation in model theory

TL;DR

This paper explores the role and connections of interpolation properties within various extensions of first-order logic using an abstract model theory approach, highlighting their relationships with other model theoretic properties.

Contribution

It provides a unified, abstract framework to analyze interpolation in diverse logical systems and clarifies its connections with properties like compactness.

Findings

Interpolation properties vary across different logical extensions.

Connections between interpolation and compactness are elucidated.

Abstract framework unifies understanding of interpolation in model theory.

Abstract

We bring an abstract model theory perspective to interpolation. We ask, what is the role of interpolation in the study of extensions of first order logic, such as infinitary logics, generalized quantifiers and higher order logics? The abstract model theory approach reveals the basic connections between various interpolation properties in isolation, on their own, as well as with respect to other model theoretic properties, such as compactness.