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CHARACTERIZATION OF POSETS OF INTERVALS

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*Judita Lihova*

**Address.** Faculty of Science, University of P.J.Safarik, 041 54 Kosice,
Jesenna 5, SLOVAKIA
**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