Type decomposition in NIP theories

TL;DR

This paper demonstrates that in NIP theories, any type can be uniquely decomposed into a stable component and a distal-like quotient, revealing a new structural insight into these theories.

Contribution

It introduces a novel type decomposition theorem in NIP theories, connecting stability and distality in a new way.

Findings

Any type in an NIP theory admits a stable-part and distal-like quotient decomposition.

The decomposition provides a new structural perspective on types in NIP theories.

This work bridges stability and distality concepts within model theory.

Abstract

We prove that any type in an NIP theory can be decomposed into a stable part (a generically stable partial type) and a distal-like quotient.