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arXiv · 2305.02648

A short note on the characterization of countable chains with finite big Ramsey spectra

Keegan Dasilva Barbosa·Dragan Mašulović·Rajko Nenadov
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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.

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Keegan Dasilva Barbosa, Dragan Mašulović, Rajko Nenadov. 2023-05-04. A short note on the characterization of countable chains with finite big Ramsey spectra. https://arxiv.org/abs/2305.02648

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