Submission date: 6 July 2020

Abstract:

In this paper, we introduce the notion of K-rank, where K is an algebraically trivial Fraisse class. Roughly speaking, the K-rank of a partial type is the number of independent “copies” of K that can be “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 well-studied ranks in model theory, including dp-rank and op-dimension.

Mathematics Subject Classification: 03C45

Keywords and phrases:

Full text arXiv 2007.02922: pdf, ps.