The model theory of metric lattices: pseudofinite partition lattices

TL;DR

This paper explores the model theory of metric lattices, introducing pseudo-finite limits of partition lattices and linking them to continuous limits, advancing the understanding of their structural properties.

Contribution

It develops a new theory of pseudo-finite limits for partition lattices within the framework of metric structures, connecting it to existing continuous limit theories.

Findings

Established a theory of pseudo-finite limits for partition lattices

Connected pseudo-finite limits with continuous limits by Björner and Lovász

Laid groundwork for further model-theoretic analysis of metric lattices

Abstract

We initiate the study of general metric lattices in the context of the model theory of metric structures. As an application we develop a theory of pseudo-finite limits of partition lattices and connect this theory with the theory of continuous limits of partition lattices due to Bj\"orner and Lov\'asz.