Naming an indiscernible sequence in NIP theories

TL;DR

This paper proves that adding a predicate for a dense indiscernible sequence to a dependent theory preserves dependence, answering a question about expansions and linear orders in NIP theories.

Contribution

It demonstrates that the expansion of a dependent theory by a predicate for a dense indiscernible sequence remains dependent, resolving a previously open question.

Findings

Adding the predicate preserves dependence in NIP theories

Every unstable dependent theory admits a dependent expansion interpreting linear order

Answers a question posed by Baldwin and Benedikt

Abstract

In this short note we show that if we add predicate for a dense complete indiscernible sequence in a dependent theory then the result is still dependent. This answers a question of Baldwin and Benedikt and implies that every unstable dependent theory has a dependent expansion interpreting linear order.