Abstract:We assign a relational structure to any finite algebra in a canonical way,
using solution sets of equations, and we prove that this relational structure
is polymorphism-homogeneous if and only if the algebra itself is
polymorphism-homogeneous. We show that polymorphism-homogeneity is also
equivalent to the property that algebraic sets (i.e., solution sets of systems
of equations) are exactly those sets of tuples that are closed under the
centralizer clone of the algebra. Furthermore, we prove that the aforemen… Show more
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