Uniqueness of constructible models in continuous logic

TL;DR

This paper proves that for any complete continuous first-order theory, all constructible models are essentially the same, differing only by an isomorphism, highlighting a fundamental uniqueness property.

Contribution

It establishes the uniqueness of constructible models in continuous logic, extending classical model theory results to the continuous setting.

Findings

Constructible models are unique up to isomorphism for any complete continuous theory.

The result generalizes classical model uniqueness to continuous logic.

Provides a foundational understanding of model structure in continuous logic.

Abstract

We show that constructible models of arbitrary complete continuous first-order theories are unique up to isomorphism.