Oscillating subalgebras of the atomless countable Boolean algebra

2025/05/28 by Dana Bartošová, David Chodounský, Bartošová, Dana +13 · 1 citation
Computer Science · #Advanced Algebra and Logic

paper · pdf · doi:10.48550/arxiv.2505.22603

Abstract

We show that the big Ramsey degree of the Boolean algebra with 3 atoms within the countable atomless Boolean algebra is infinite.

Citations

• Counting big Ramsey degrees of the homogeneous and universal K₄-free graph
• On Big Ramsey degrees of universal ω-edge-labeled hypergraphs
• Oscillation stability by the Carlson-Simpson theorem
• A survey on big Ramsey structures
• Ramsey theorem for trees with successor operation
• Big Ramsey degrees in the metric setting
• Type-respecting amalgamation and big Ramsey degrees
• Exact big Ramsey degrees for finitely constrained binary free amalgamation classes
• Big Ramsey degrees and forbidden cycles
• Dual Ramsey properties for classes of algebras
• Big Ramsey degrees using parameter spaces
• On big Ramsey degrees for binary free amalgamation classes
• Big Ramsey degrees of 3-uniform hypergraphs
• The Ramsey Theory of Henson graphs
• Forcing in Ramsey theory
• The Ramsey theory of the universal homogeneous triangle-free graph Part\n II: Exact big Ramsey degrees
• Big Ramsey degrees and topological dynamics
• The oscillation stability problem for the Urysohn sphere: A combinatorial approach
• Twenty years of Nešetřil's classification programme of Ramsey classes

Cited by

• On Big Ramsey degrees of universal ω-edge-labeled hypergraphs

Related

• A complete Boolean algebra that has no proper atomless complete subalgebra
• Notes on countably generated complete Boolean algebras
• Functional reducts of Boolean algebras
• Embeddings into the countable atomless Boolean algebra
• Superatomic Boolean Algebras: maximal rigidity