Additivity of the dp-rank
Itay Kaplan, Alf Onshuus, and Alexander Usvyatsov
TL;DR
This paper proves that dp-rank is sub-additive, explores the limitations of reducing finite dp-rank theories to dp-minimal types, and discusses potential links between dp-rank and VC-density.
Contribution
It establishes the sub-additivity of dp-rank and analyzes the relationship between finite dp-rank theories, dp-minimal types, and VC-density.
Findings
Dp-rank is sub-additive.
Finite dp-rank theories cannot be fully understood through dp-minimal types.
Potential connections between dp-rank and VC-density are discussed.
Abstract
The main result of this article is sub-additivity of the dp-rank. We also show that the study of theories of finite dp-rank can not be reduced to the study of its dp-minimal types, and discuss the possible relations between dp-rank and VC-density.
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Taxonomy
TopicsAdvanced Topology and Set Theory · Rings, Modules, and Algebras · Fuzzy and Soft Set Theory