The order-sum in classes of partially ordered algebras

Let [cursive R] be a class of partially ordered algebras, T a partially ordered set. A family of homomorphisms [Phi][lowered t] : P[lowered t]------- >P, where P, P[lowered t][epsilon][cursive R], is called a T-family provided that [Phi]lowered s<[Phi][lowered t(y) in P, for all x[epsilon]P[lowered s], y[epsilon]P[lowered t], whenever s<t in T...