Exact big Ramsey degrees for finitely constrained binary free amalgamation classes
Exact big Ramsey degrees for finitely constrained binary free amalgamation classes
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发表时间：
2021-10
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通讯作者：
M. Balko;David Chodounsk'y;Natasha Dobrinen;Jan Hubivcka;Matvej Konevcn'y;Lluís Vena;Andy Zucker
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作者：
M. Balko;David Chodounsk'y;Natasha Dobrinen;Jan Hubivcka;Matvej Konevcn'y;Lluís Vena;Andy Zucker
本文刻画了由许多禁止不可约子结构定义的有限二元语言中自由合并类的大Ramsey度，从而改进了Zucker最近给出的上界.利用这一刻画，我们证明了每个类的Fra\“iss\”e极限都有一个强的大Ramsey结构，这意味着Fra\“iss\”e极限的自同构群有一个可度量化的泛完备流.
We characterize the big Ramsey degrees of free amalgamation classes in finite binary languages defined by finitely many forbidden irreducible substructures, thus refining the recent upper bounds given by Zucker. Using this characterization, we show that the Fra\"iss\'e limit of each such class admits a strong big Ramsey structure, implying that the automorphism group of the Fra\"iss\'e limit has a metrizable universal completion flow.