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 Nešetřil and Rödl in 1984). Towards this, we refine earlier upper bounds obtained by Hubička 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.
Fields of Study & Subjects
Advanced Topology and Set Theory
Computability
Logic
AI Algorithms
semigroups and automata theory
Publication details
- Journal / source
- Transactions of the American Mathematical Society
- Publisher
- American Mathematical Society (AMS)
- Volume
- 379
- Issue
- 10
- Pages
- 6921–6951
- Publication date
- 1 July 2026
- Language
- EN