Generically stable regular types

TL;DR

This paper investigates the properties of symmetric, regular types in model theory, demonstrating that non-orthogonality preserves generic stability and forms an equivalence relation, while also relating strongly regular types to the Rudin-Keisler order.

Contribution

It establishes that non-orthogonality preserves generic stability and is an equivalence relation among regular types, extending stable properties to a broader context.

Findings

Non-orthogonality preserves generic stability.

Non-orthogonality is an equivalence relation among regular types.

Connections between strongly regular types and the Rudin-Keisler order.

Abstract

We study non-orthogonality of symmetric, regular types and show that it preserves generic stability and is an equivalence relation on the set of all generically stable, regular types. We will also prove that some of the nice properties from the stable context hold in general. In the case of strongly regular types we will relate non-orthogonality to the global Rudin-Keisler order.