If $A$ is a class of partially ordered sets, let $P(A)$ denote the system of all posets which are isomorphic to the system of all intervals of $A$ for some $A\in A.$ We give an algebraic characterization of elements of $P(A)$ for $A$ being the class of all bounded posets and the class of all posets $A$ satisfying the condition that for each $a\in A$ there exist a minimal element $u$ and a maximal element $v$ with $u\le a\le v,$ respectively.
@article{107729,
author = {Judita Lihov\'a},
title = {Characterization of posets of intervals},
journal = {Archivum Mathematicum},
volume = {036},
year = {2000},
pages = {171-181},
zbl = {1047.06002},
mrnumber = {1785034},
language = {en},
url = {http://dml.mathdoc.fr/item/107729}
}
Lihová, Judita. Characterization of posets of intervals. Archivum Mathematicum, Tome 036 (2000) pp. 171-181. http://gdmltest.u-ga.fr/item/107729/
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