Ranks based on strong amalgamation Fraisse classes

In this paper, we introduce the notion of K-rank, where K is a strong amalgamation Fraisse class. Roughly speaking, the K-rank of a partial type is the number copies of K that can be independently coded inside of the type. We study K-rank for specific examples of K, including linear orders, equivalence relations, and graphs. We discuss the relationship of K-rank to other ranks in model theory, including dp-rank and op-dimension (a notion coined by the first author and C. D. Hill in previous work).

Automated summary

In this paper, the concept of K-rank is introduced, where K is a strong amalgamation Fraisse class. The K-rank of a partial type is essentially the number of independent copies of K that can be coded within the type. The paper explores K-rank in specific examples such as linear orders, equivalence relations, and graphs, and discusses its relationship with other ranks in model theory, including dp-rank and op-dimension (a notion coined by the authors in previous work).