Characterizing Model-Theoretic Dividing Lines via Collapse of Generalized Indiscernibles

TL;DR

This paper introduces a novel approach using collapse of generalized indiscernible sequences to classify key model-theoretic dividing lines, providing new characterizations for properties like op-dimension, rosiness, and NTP2.

Contribution

It develops a unified framework linking indiscernible collapse phenomena to various dividing lines in model theory, offering new characterizations for these properties.

Findings

Collapse of n-multi-order indiscernibles characterizes op-dimension n

Collapse of function-space indiscernibles characterizes rosy theories

Collapse of convex equivalence relation indiscernibles characterizes NTP2 theories

Abstract

We use the notion of collapse of generalized indiscernible sequences to classify various model theoretic dividing lines. In particular, we use collapse of n-multi-order indiscernibles to characterize op-dimension n; collapse of function-space indiscernibles (i.e. parameterized equivalence relations) to characterize rosy theories; and finally, convex equivalence relation indiscernibles to characterize NTP2 theories.