As a result of 33 intercontinental Zoom calls, we characterise big Ramsey degrees of the generic partial order. This is an infinitary extension of the well known fact that finite partial orders endowed with linear extensions form a Ramsey class (this result was announced by Ne\v set\v ril and R\"odl in 1984 with first published proof by Paoli, Trotter and Walker in 1985). Towards this, we refine earlier upper bounds obtained by Hubi\v cka based on a new connection of big Ramsey degrees to the Carlson--Simpson theorem and we also introduce a new technique of giving lower bounds using an iterated application of the upper-bound theorem.
翻译:基于33次跨洲Zoom通话,我们刻画了一般偏序的大Ramsey度。这是对有限偏序在线性扩张下构成Ramsey类这一已知结论的无穷推广(该结论由Nešetřil和Rödl于1984年提出,首个证明由Paoli、Trotter和Walker于1985年发表)。为此,我们改进了Hubička基于大Ramsey度与Carlson-Simpson定理新关联所建立的早期上界,并引入一种利用上界定理迭代应用给出下界的新技术。