Infinitary Baker–Pixley theorem

n important theorem of Baker and Pixley states that if 𝐀 is a finite algebra with a (d+1) -ary near-unanimity term and f is an n -ary operation on A such that every subalgebra of 𝐀^d is closed under f , then f is representable by a term in 𝐀 . It is well known that the Baker–Pixley theorem does not hold when 𝐀 is infinite. We give an infinitary version of the Baker–Pixley theorem which applies to an arbitrary class of structures with a (d+1) -ary near-unanimity term instead of a single finite algebra.