Geodesic
The number of linear orders on a~field
Matematičeskie zametki, Tome 6 (1969) no. 2, pp. 201-211.

Voir la notice de l'article provenant de la source Math-Net.Ru

An example is given of a field which can be ordered in exactly $\aleph$ ways where $\aleph$ is a given cardinal number. 
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Yu. L. Ershov. The number of linear orders on a~field. Matematičeskie zametki, Tome 6 (1969) no. 2, pp. 201-211. http://geodesic.mathdoc.fr/item/MZM_1969_6_2_a8/