It is consistent that there exists an ordered real closed field which is not hyper-real.
Stojanović, Jadran ; Perović, Žikica
Publications de l'Institut Mathématique. Nouvelle Série, Tome 61(75) (1997), p. 17-20 / Harvested from The Electronic Library of Mathematics
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Publié le : 1997-01-01
MISANU-ID : j_publ_0001753
EUDML-ID : urn:eudml:doc:258031 
@article{01200270,
     title = {It is consistent that there exists an ordered real closed field which is not hyper-real.},
     journal = {Publications de l'Institut Math\'ematique. Nouvelle S\'erie},
     volume = {61(75)},
     year = {1997},
     pages = {17-20},
     zbl = {0999.12501},
     language = {en},
     url = {http://dml.mathdoc.fr/item/01200270}
}

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, Tome 61(75) (1997) pp. 17-20. http://gdmltest.u-ga.fr/item/01200270/