Partition properties of the dense local order and a colored version of Milliken's theorem


We study finite dimensional partition properties of the countable homogeneous dense local order (a directed graph closely related to the order structure of the rationals). Some of our results use ideas borrowed from the partition calculus of the rationals and are obtained thanks to a strengthening of Milliken’s theorem on trees. 
DOI: 10.1007/s00493-010-2445-y


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