Big Ramsey degrees and divisibility in classes of ultrametric spaces
L. Nguyen Van Th\'e
TL;DR
This paper investigates the finite-dimensional Ramsey properties of the countable ultrametric Urysohn space with distances in a specified set of positive reals, exploring its divisibility and structural features.
Contribution
It introduces new Ramsey-theoretic results for ultrametric spaces with distances in a given set, advancing understanding of their combinatorial and divisibility properties.
Findings
Established finite-dimensional Ramsey properties for the space
Identified divisibility characteristics of the ultrametric Urysohn space
Extended classical results to a broader class of ultrametric spaces
Abstract
Given a countable set S of positive reals, we study finite-dimensional Ramsey-theoretic properties of the countable ultrametric Urysohn space with distances in S.
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