Thorn-Forking in Continuous Logic

TL;DR

This paper investigates thorn forking and rosiness within continuous logic, demonstrating that the Urysohn sphere is rosy and establishing new results about rosiness and elimination of imaginaries in continuous and classical theories.

Contribution

It proves the Urysohn sphere is rosy in continuous logic and shows that weak elimination of finitary imaginaries implies rosiness with respect to them, a novel result.

Findings

Urysohn sphere is rosy in continuous logic

Rosiness with respect to finitary imaginaries follows from weak elimination

First example of an unstable continuous theory with a well-behaved independence notion

Abstract

We study thorn forking and rosiness in the context of continuous logic. We prove that the Urysohn sphere is rosy (with respect to finitary imaginaries), providing the first example of an essentially continuous unstable theory with a nice notion of independence. In the process, we show that a real rosy theory which has weak elimination of finitary imaginaries is rosy with respect to finitary imaginaries, a fact which is new even for classical real rosy theories.