Characterisation of the big Ramsey degrees of the generic partial order
Abstract
As a result of 33 intercontinental Zoom calls, we characterise big Ramsey degrees of the generic partial order. This is an infinitary extension of the well known fact that finite partial orders endowed with linear extensions form a Ramsey class (this result was announced by Ne\v{s}et\v{r}il and R\"odl in 1984 with first published proof by Paoli, Trotter and Walker in 1985). Towards this, we refine earlier upper bounds obtained by Hubi\v{c}ka based on a new connection of big Ramsey degrees to the Carlson-Simpson theorem and we also introduce a new technique of giving lower bounds using an iterated application of the upper-bound theorem.
Keywords
Cite
@article{arxiv.2303.10088,
title = {Characterisation of the big Ramsey degrees of the generic partial order},
author = {Martin Balko and David Chodounský and Natasha Dobrinen and Jan Hubička and Matěj Konečný and Lluis Vena and Andy Zucker},
journal= {arXiv preprint arXiv:2303.10088},
year = {2025}
}
Comments
28 pages, 7 figures. Minor revision fixing typos and updating bibliography. Accepted to Transactions of the American Mathematical Society