An $\mathrm{NSOP}_{1}$ theory without the existence axiom

TL;DR

This paper constructs an $ ext{NSOP}_1$ theory that notably lacks the existence axiom, answering a specific open question in model theory.

Contribution

It provides the first example of an $ ext{NSOP}_1$ theory without the existence axiom, advancing understanding of the properties of such theories.

Findings

Existence axiom can fail in $ ext{NSOP}_1$ theories.

First known example of an $ ext{NSOP}_1$ theory without existence.

Answers a question posed by Dobrowolski, Kim, and Ramsey.

Abstract

Answering a question of Dobrowolski, Kim and Ramsey, we find an $\mathrm{NSOP}_{1}$ theory that does not satisfy the existence axiom.