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Big Ramsey Degrees of 3-Uniform Hypergraphs are Finite
Combinatorica ( IF 1.1 ) Pub Date : 2022-02-18 , DOI: 10.1007/s00493-021-4664-9
Martin Balko 1 , David Chodounský 1 , Jan Hubička 1 , Matěj Konečný 1 , Lluis Vena 2
Affiliation  

We prove that the universal homogeneous 3-uniform hypergraph has finite big Ramsey degrees. This is the first case where big Ramsey degrees are known to be finite for structures in a non-binary language.

Our proof is based on the vector (or product) form of Milliken’s Tree Theorem and demonstrates a general method to carry existing results on structures in binary relational languages to higher arities.



中文翻译:

3-均匀超图的大 Ramsey 度数是有限的

我们证明了通用齐次 3-一致超图具有有限的大 Ramsey 度。这是第一个已知大 Ramsey 度数对于非二进制语言中的结构是有限的情况。

我们的证明基于米利肯树定理的向量(或乘积)形式,并演示了一种将二进制关系语言中结构的现有结果传递给更高元的通用方法。

更新日期:2022-02-18
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