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Uniqueness of constructible models in continuous logic

James E. Hanson

TL;DR

The paper addresses the uniqueness of constructible models in complete continuous first-order theories, extending Ressayre-style results to the continuous setting. It introduces augmented construction sequences to track distance predicates and definability, and develops self-sufficiency and a dense back-and-forth framework to glue finite segments into a global isomorphism. The main result proves that any two constructible models of the same complete theory are isomorphic (over a base parameter set, if specified). This generalizes classical model-theoretic uniqueness to continuous logic and provides a robust method for stability-theoretic analysis in this context.

Abstract

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

Uniqueness of constructible models in continuous logic

TL;DR

The paper addresses the uniqueness of constructible models in complete continuous first-order theories, extending Ressayre-style results to the continuous setting. It introduces augmented construction sequences to track distance predicates and definability, and develops self-sufficiency and a dense back-and-forth framework to glue finite segments into a global isomorphism. The main result proves that any two constructible models of the same complete theory are isomorphic (over a base parameter set, if specified). This generalizes classical model-theoretic uniqueness to continuous logic and provides a robust method for stability-theoretic analysis in this context.

Abstract

We show that constructible models of arbitrary complete continuous first-order theories are unique up to isomorphism.
Paper Structure (3 sections, 14 theorems)

This paper contains 3 sections, 14 theorems.

Table of Contents

  1. Augmented construction sequences
  2. Self-sufficiency
  3. Uniqueness of constructible models

Key Result

Theorem 2

Any two constructible models of a complete theory are isomorphic.

Theorems & Definitions (33)

  • Definition 1
  • Theorem 2: Ressayre
  • Lemma 1.1
  • proof
  • Definition 1.2
  • Definition 1.3
  • Lemma 1.4
  • proof
  • Definition 1.5
  • Lemma 1.6
  • ...and 23 more