A Poset is an interval order if it is Isomorphic to some set of Intervals on the Real Line ordered by left-to-right precedence. Formally, is an interval order provided that one can assign to each an Interval such that in the Real Numbers Iff in .
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.