For n ? ?, a relation ? ? A? is algebraic over a clone F on A if there is a set I and f?, g? ? F??? for i ? I such that
? = { x ? A? | ? i ? I?f?(x) = g?(x) }.
A clone F on A is equationally additive if the union of any two of its algebraic relations of the same arity is again algebraic. In the talk we shall describe all equationally additive Boolean clones, and we shall investigate the number of equationally additive clones on larger finite sets.
Joint work with Erhard Aichinger and Bernardo Rossi (JKU Linz) and funded by FWF project P33878.
Forschungs-