2025/12/05 by Cameron, Peter J., Lashkarighouchani, Siavash
#05C55 #Combinatorics (math.CO) #FOS: Mathematics #Logic (math.LO)
paper · doi:10.48550/arxiv.2512.05684
The celebrated theorem of Kechris, Pestov and Todorčević connecting structural Ramsey theory with topological dynamics has as a consequence that the Fra"ıssé limit of a Ramsey class of non-trivial finite relational structures has a reduct which is a total order; this implies an earlier result of Nešetřil, according to which the structures in such a class are rigid (have trivial automorphism groups). In this paper, we give an alternative proof of this fact. If C is a Fra"ıssé class of rigid structures over a finite relational language, then either the Fra"ıssé limit of C has a reduct which is a total order, or there is an explicit failure of the Ramsey property involving a pair (A,B) of structures in C with |A|=2.