Geodesic
Which Ordered Sets have a Complete Linear Extension?
Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1245-1254

Voir la notice de l'article provenant de la source Cambridge University Press

It is a well known and useful fact [4] that every (partially) ordered set P has a linear extension L (that is, a totally ordered set (chain) on the same underlying set as P and satisfying a ≦ b in L whenever a ≦ b in P). It is just as well known that an ordered set P can be embedded in an ordered set P′ which, in turn, has a complete linear extension L′ (that is, a linear extension in which every subset has both a supremum and an infimum); just take L′ to be the “completion by cuts” of L. However, an arbitrary ordered set P need not, itself, have a complete linear extension (for example, if P is the chain of integers or, for that matter, if P is any noncomplete chain). It is natural to ask which ordered sets have a complete linear extension? 
Pouzet, Maurice; Rival, Ivan. Which Ordered Sets have a Complete Linear Extension?. Canadian journal of mathematics, Tome 33 (1981) no. 5, pp. 1245-1254. doi: 10.4153/CJM-1981-093-9
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