A short note on the characterization of countable chains with finite big Ramsey spectra
Logic
2023-07-25 v2 Combinatorics
Abstract
In this short note we confirm the deep structural correspondence between the complexity of a countable scattered chain (= strict linear order) and its big Ramsey combinatorics: we show that a countable scattered chain has finite big Ramsey degrees if and only if it is of finite Hausdorff rank. This also provides a complete characterization of countable chains whose big Ramsey spectra are finite. We expand the notion of big Ramsey spectrum to monomorphic structures and give a sufficient condition for a monomorphic countable structure to have finite big Ramsey spectrum.
Keywords
Cite
@article{arxiv.2305.02648,
title = {A short note on the characterization of countable chains with finite big Ramsey spectra},
author = {Keegan Dasilva Barbosa and Dragan Mašulović and Rajko Nenadov},
journal= {arXiv preprint arXiv:2305.02648},
year = {2023}
}