Behrisch, M., Aichinger, E., & Rossi, B. (2022, June 25). On equationally additive clones [Conference Presentation]. AAA 102 - 102nd Workshop on General Algebra, Szeged, Hungary. https://doi.org/10.34726/3046
Clone; Boolean clone; equationally additive; algebraic set
en
Abstract:
For n ∈ ℕ, a relation ϱ ⊆ Aⁿ is algebraic over a clone F on A if there is a set I and fᵢ, gᵢ ∈ F⁽ⁿ⁾ for i ∈ I such that ϱ = { x ∈ Aⁿ | ∀ i ∈ I:fᵢ(x) = gᵢ(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 ofequationally additive clones on larger finite sets.