TL;DR
This paper proves that in NTP_2 theories, dependent types with high or infinite dp-rank can be witnessed by indiscernible sequences or singletons, respectively, advancing understanding of dp-rank in model theory.
Contribution
It establishes that high dp-rank types in NTP_2 theories can be witnessed by indiscernible sequences or singletons, providing new insights into dp-rank characterization.
Findings
Dependent types with dp-rank >= κ can be witnessed by indiscernible sequences.
Types with infinite dp-rank can be witnessed by singletons.
Results apply specifically within NTP_2 theories.
Abstract
We prove that in NTP_2 theories if p is a dependent type with dp-rank >= \kappa, then this can be witnessed by indiscernible sequences of tuples satisfying p. If p has dp-rank infinity, then this can be witnessed by singletons (in any theory).
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