ИСТИНА

C-clones are clones that can be described as polymorphism sets of relations of the form Rab = {(x, y) ∈ Dp+q | (∃1 ≤ i ≤ p: xi ≥ ai) ∨(∃1 ≤ j ≤ q: yj ≤ bj)}, where the tuples a ∈ Dp and b ∈ Dq are parameters for some p, q > 0, and where ≤ denotes the canonical linear order on the finite set D={0, ..., n-1}. As clones in general, also C-clones form a complete lattice w.r.t. set inclusion. It is known from previous work that for n = 2 there are exactly five such clones and that their number is infinite, whenever n ≥ 3. In the talk we answer the open question after the exact cardinality of the lattice of C-clones: by relating it to the number of downsets of (N, ≤ )m we show that the cardinality is countably infinite.