E-mail: lihova@duro.science.upjs.sk
Abstract. If $\eusm A$ is a class of partially ordered sets, let $\eusm P(\eusm A)$ denote the system of all posets which are isomorphic to the system of all intervals of $\Bbb A$ for some $\Bbb A\in\eusm A.$ We give an algebraic characterization of elements of $\eusm P(\eusm A)$ for $\eusm A$ being the class of all bounded posets and the class of all posets $\Bbb A$ satisfying the condition that for each $a\in \Bbb A$ there exist a minimal element $u$ and a maximal element $v$ with $u\leq a\leq v,$ respectively.
AMSclassification. 06A06
Keywords. Partially ordered set, interval