Given a (countable) set of variables Var, we call a supported algebra a pair (A, spp), where A is an algebra and spp is a relation between subsets of Var and elements of A such that
- every set (X: X spp a) is a filter on Var, and
- every set (a: X spp a) is a subalgebra of A.
Here, elements of A are thought of as depending on variables. Where X spp a, we say that X is a support of a; in this case, a does not depend on variables outside of X. We characterize those supported algebras which can be represented by certain algebras of functions. The problem comes from algebraic logic.