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math.LO2023
Infinite-dimensional Ramsey theory for binary free amalgamation classes
Natasha Dobrinen, Andy Zucker
We develop infinite-dimensional Ramsey theory for Fraïssé limits of finitely constrained free amalgamation classes in finite binary languages. We show that our approach is optimal…
math.LO2022
Polish space partition principles and the Halpern-Läuchli theorem
Chris Lambie-Hanson, Andy Zucker
The Halpern-Läuchli theorem, a combinatorial result about trees, admits an elegant proof due to Harrington using ideas from forcing. In an attempt to distill the combinatorial esse…
math.LO2017
Big Ramsey degrees and topological dynamics
Andy Zucker
We consider Fraïssé structures whose objects have finite big Ramsey degree and ask what consequences this has for the dynamics of the automorphism group. Motivated by a theorem of…