Continuous first order logic and local stability

TL;DR

This paper develops continuous first order logic, extending existing frameworks and demonstrating its suitability for local stability analysis in structures like Banach spaces.

Contribution

It introduces continuous first order logic, showing its equivalence to open Hausdorff cats and extending Henson's logic for Banach spaces.

Findings

Continuous logic has the same expressive power as open Hausdorff cats.

The logic extends Henson's logic for Banach space structures.

It is particularly well-suited for developing local stability theory.

Abstract

We develop continuous first order logic, a variant of the logic described in \cite{Chang-Keisler:ContinuousModelTheory}. We show that this logic has the same power of expression as the framework of open Hausdorff cats, and as such extends Henson's logic for Banach space structures. We conclude with the development of local stability, for which this logic is particularly well-suited.