Oscillating subalgebras of the atomless countable Boolean algebra
Dana Barto\v{s}ov\'a, David Chodounsk\'y, Barbara Csima, Jan Hubi\v{c}ka, Mat\v{e}j Kone\v{c}n\'y, Joey Lakerdas-Gayle, Spencer Unger, Andy Zucker
TL;DR
This paper investigates the big Ramsey degrees within the countable atomless Boolean algebra, revealing that the degree for the algebra with three atoms is infinite, highlighting complex combinatorial properties.
Contribution
It establishes that the big Ramsey degree of the Boolean algebra with three atoms in the atomless case is infinite, providing new insights into the structure's combinatorial complexity.
Findings
Big Ramsey degree of 3-atom Boolean algebra is infinite
Highlights complexity in atomless Boolean algebra structures
Advances understanding of Ramsey theory in algebraic contexts
Abstract
We show that the big Ramsey degree of the Boolean algebra with 3 atoms within the countable atomless Boolean algebra is infinite.
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Taxonomy
TopicsAdvanced Algebra and Logic