Infinitary Baker–Pixley theorem

An 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.