Local-to-global cyclic polymorphism conjecture for omega-categorical cores

Let B{\mathfrak B} be a countable ω\omega-categorical model-complete core, and let ff be an nn-ary polymorphism of B{\mathfrak B}. Cyclic polymorphism conjecture. If, for every finite subset AA of the domain of B{\mathfrak B}, there is an endomorphism ee satisfying f(x1,,xn)=e(f(x2,,xn,x1))f(x_1,\dots,x_n)=e(f(x_2,\dots,x_n,x_1)) for all x1,,xnAx_1,\dots,x_n\in A, then B{\mathfrak B} has a cyclic polymorphism modulo an endomorphism. The source does not state whether this local-to-global principle has been resolved.

Sources & referencesView supporting material

Primary source

Manuel Bodirsky, “Complexity Classification in Infinite-Domain Constraint Satisfaction”, arXiv:1201.0856 (2019).

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