On forking and definability of types in some dp-minimal theories

TL;DR

This paper investigates the structure of types in dp-minimal theories, showing that in many such theories including p-adics, definable types are densely present among non-forking types, enhancing understanding of their model-theoretic properties.

Contribution

It establishes that in a broad class of dp-minimal theories, definable types are dense among non-forking types, extending known results to p-adic and similar theories.

Findings

Definable types are dense among non-forking types in many dp-minimal theories.

Includes the p-adics as a key example of these theories.

Provides new insights into the structure of types in dp-minimal theories.

Abstract

We prove in particular that, in a large class of dp-minimal theories including the p-adics, definable types are dense amongst non-forking types.