Transitive sets

One paper in Euclidean Ramsey theory is “Transitive sets in Euclidean Ramsey theory” by Imre Leader, Paul A. Russell and Mark Walters. A set is transitive if its symmetry group of isometries is transitive. The paper looks at the question what if only transitive sets are Ramsey. It is known that Ramsey sets are spherical and it has been conjectured that all spherical sets are Ramsey. The paper shows that the conjectures are not equivalent that there exist sets that are spherical and cannot be embedded in any transitive set. It also looks at equivalent forms of the statement all transiive sets are Ramsey. It is here. I may talk further about the questions raised in this paper in future posts as there are some other papers written in response to these questions


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