Interval Order

A Poset $P = (X, \leq)$ is an interval order if it is Isomorphic to some set of Intervals on the Real Line ordered by left-to-right precedence. Formally, $P$ is an interval order provided that one can assign to each $x \in X$ an Interval $[x_L, x_R]$ such that $x_R < y_L$ in the Real Numbers Iff $x<y$ in $P$.

See also Partially Ordered Set

References

Fishburn, P. C. Interval Orders and Interval Graphs: A Study of Partially Ordered Sets. New York: Wiley, 1985.

Wiener, N. ``A Contribution to the Theory of Relative Position.'' Proc. Cambridge Philos. Soc. 17, 441-449, 1914.