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Conjectures for clones over finitely bounded homogenous structures Pinsker, Michael


There has been a conjectured criterion, by Manuel Bodirsky and myself, for when deciding the truth of a primitive positive sentence over a reduct of a finitely bounded homogeneous structure is tractable. This criterion has recently been replaced by a seemingly better criterion, although the equivalence of the two criteria is an open problem. We discuss the two conjectures, their relation, and further related conjectures and thoughts.

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