Saturated Models for the Working Model Theorist

TL;DR

This paper discusses the practical assumption of saturated models in model theory, showing that it generally does not cause issues for most applications, and is accessible to those with basic set theory knowledge.

Contribution

It formalizes a classical result, clarifying that assuming saturated models is often harmless for model theorists.

Findings

Saturated models can be assumed without loss of generality in most model-theoretic contexts.

The paper provides a clear, accessible presentation of the classical result.

It bridges the gap between abstract theory and practical application in model theory.

Abstract

We put in print a classical result that states that for most purposes, there is no harm in assuming the existence of saturated models in model theory. The presentation is aimed for model theorists with only basic knowledge of axiomatic set theory.