On Finite Maximal Antichains in the Homomorphism Order

Dualities and Dual Pairs in Heyting Algebras

“…In particular, if B ∩ ↓A = ∅, it can be split into two subsets (A and B) so that every element of L \ C is above A or below B. This fact has a direct connection to the splitting property of posets (see [1,2,6,9,10,11,13]). Indeed, in [14] it is proved that finite maximal antichains in the poset arising from the category C of relational structures with one relation contain no elements of ↓wld( C) \ wld( C).…”

No Finite–Infinite Antichain Duality in the Homomorphism Poset of Directed Graphs

“…This particularly useful instance of the antichain duality was introduced by Nešetřil and Pultr in [14]. Clearly, F, D ∈ D × D is a duality pair if Foniok, Nešetřil and Tardif studied a generalization of the notion of single duality pairs, which is another special case of antichain dualities [6][7][8]: a generalized duality pair is an antichain duality F, D such that both F and D are finite. The generalized duality pairs (in the much more general context of homomorphism poset of relational structures) are characterized in [7].…”