Countable structures admitting finite monomorphic decomposition have finite big Ramsey degrees iff their monomorphic parts do, via chainability and Laver's theorem on Fraïssé's conjecture.
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Fra\"{i}ss\'{e}'s Conjecture and big Ramsey degrees of structures admitting finite monomorphic decomposition
Countable structures admitting finite monomorphic decomposition have finite big Ramsey degrees iff their monomorphic parts do, via chainability and Laver's theorem on Fraïssé's conjecture.