Effective clones
A clone on a base set X is a set C of operations (functions from some finite power of X into X) which contains all the projection functions and is closed under composition (e.g, the set of all pointwise monotone operations on a partial order X, or the set of all polynomials on a ring X). Already on a 3-element set there are countably many operations and uncountably many clones.
A clone C can be described "from above", by specifying the relations that all functions from C preserve (e.g., monotone functions preserve the given partial order, as well as the opposite order) or "from below" (e.g., the set of polynomials is the smallest clone containing all constant functions plus addition and multiplication).
I will discuss the set of clones on a given finite or infinite base set, with particular emphasis on clones that that are in some sense "effective" -- closed clones (also called local clones), finitely generated clones, clones defined by a single relation, etc.
