It is consistent that there exists an ordered real closed field which is not hyper-real.
Publications de l 'Institut Mathématique. Nouvelle Série, 61(75) (1997), p. 17.

Voir la notice de l'article dans European Digital Mathematics Library

Classification : 12J15, 03C60, 03E05
Mots-clés : hyper-real fields, -ordered field, models of ZFC, -ordered field 
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Stojanović, Jadran; Perović, Žikica. It is consistent that there exists an ordered real closed field which is not hyper-real.. Publications de l 'Institut Mathématique. Nouvelle Série, 61(75) (1997), p. 17. https://geodesic-test.mathdoc.fr/item/PIM2_1997__61(75)_258031/